Operation of Functions
Summary
TLDRIn this educational video, Teacher SP explains the four fundamental operations of functions: addition, subtraction, multiplication, and division. The video provides clear examples of how to evaluate these operations, emphasizing the importance of not dividing by zero. The teacher demonstrates with functions f(x) = x - 3 and g(x) = x + 5, showing how to perform the operations and simplify the results. The lesson is designed to help viewers understand and apply these operations to functions effectively.
Takeaways
- 📚 The video discusses the fundamental operations of functions, focusing on addition, subtraction, multiplication, and division.
- 🔢 Addition of functions is defined as the sum of f(x) and g(x), represented as f(x) + g(x).
- ➖ Subtraction of functions is defined as the difference of f(x) and g(x), represented as f(x) - g(x).
- 🔄 Multiplication of functions is defined as the product of f(x) and g(x), represented as f(x) * g(x).
- 🔄 Division of functions is defined as the quotient of f(x) and g(x), represented as f(x) / g(x), with the caveat that g(x) cannot be zero to avoid undefined results.
- ❌ Division by zero is emphasized as undefined, using the example of eight divided by zero.
- 📘 An example is provided to demonstrate the operations: f(x) = x - 3 and g(x) = x + 5, showing how to apply the four operations.
- 🧮 For addition, the example simplifies to 2x + 2, and then factors out to 2(x + 1).
- 📉 For subtraction, the example results in -8 after applying the rules of integer subtraction.
- 📊 For multiplication, the example uses the FOIL method for binomials, resulting in x^2 + 2x - 15.
- 📌 For division, the example shows that binomials cannot be directly divided or cancelled out in the context of the operations discussed.
Q & A
What are the four fundamental operations of functions?
-The four fundamental operations of functions are addition, subtraction, multiplication, and division.
How is the sum of two functions f(x) and g(x) defined?
-The sum of two functions f(x) and g(x) is defined as f(x) + g(x).
What is the difference between the functions f(x) and g(x) when f(x) is 10 and g(x) is 2?
-The difference between the functions f(x) and g(x) when f(x) is 10 and g(x) is 2 is 8, as 10 - 2 equals 8.
What is the product of the functions f(x) and g(x) when f(x) is 3 and g(x) is 5?
-The product of the functions f(x) and g(x) when f(x) is 3 and g(x) is 5 is 15, as 3 times 5 equals 15.
Why is division by g(x) not allowed when g(x) equals zero?
-Division by g(x) is not allowed when g(x) equals zero because it results in an undefined expression, as division by zero is undefined in mathematics.
What is the result when you add the functions f(x) = x - 3 and g(x) = x + 5?
-The result when you add the functions f(x) = x - 3 and g(x) = x + 5 is 2x + 2, after simplifying the expression.
How do you find the difference between the functions f(x) = x - 3 and g(x) = x + 5?
-To find the difference between the functions f(x) = x - 3 and g(x) = x + 5, you subtract g(x) from f(x), resulting in -8 after applying the subtraction rules.
What is the product of the binomials (x - 3) and (x + 5) using the FOIL method?
-Using the FOIL method, the product of the binomials (x - 3) and (x + 5) is x^2 - 3x + 5x - 15, which simplifies to x^2 + 2x - 15.
Why can't you directly divide the binomials (x - 3) by (x + 5)?
-You can't directly divide the binomials (x - 3) by (x + 5) because they are not in a form that allows for simple cancellation or direct division as they are both binomials.
What is the final simplified form of the expression 2x + 2 after factoring out the common factor?
-The final simplified form of the expression 2x + 2 after factoring out the common factor 2 is 2(x + 1).
Outlines
📘 Introduction to Operations of Functions
Teacher SP begins the video by welcoming viewers back to the channel and encourages them to subscribe, like, comment, and enable notifications. The main topic of the video is the fundamental operations of functions, which include addition, subtraction, multiplication, and division. The instructor explains each operation using simple arithmetic examples and then relates them to functions. For addition, the sum of functions f(x) and g(x) is defined as f(x) + g(x). For subtraction, it's f(x) - g(x), for multiplication, it's f(x) * g(x), and for division, it's f(x) / g(x), with the caveat that g(x) must not equal zero to avoid undefined results. The instructor also clarifies why division by zero is undefined using an example of eight divided by zero. The video aims to provide a clear understanding of how to evaluate these operations with functions.
🔢 Applying Operations to Functions
In this segment, the instructor applies the four fundamental operations to specific functions f(x) = x - 3 and g(x) = x + 5. For addition, the instructor combines the functions to get (x - 3) + (x + 5), which simplifies to 2x + 2. The common factor of 2 is then factored out, resulting in the final answer of 2(x + 1). For subtraction, the instructor follows the rule of changing the sign of the subtrahend, leading to the result of -8 after simplification. For multiplication, the FOIL method is used to multiply (x - 3) and (x + 5), resulting in x^2 - 3x + 5x - 15, which simplifies to x^2 + 2x - 15. Lastly, for division, the instructor notes that the binomials (x - 3) and (x + 5) cannot be directly divided or canceled out, indicating that the expression stands as the final answer for division. The video concludes with a reminder that the next lesson will cover more complex equations involving these operations.
Mindmap
Keywords
💡Operations of Functions
💡Addition
💡Subtraction
💡Multiplication
💡Division
💡Undefined
💡Binomials
💡FOIL Method
💡Common Factor
💡Cancellation
💡Fundamental Operations
Highlights
Introduction to the concept of operations of functions.
Definition of the four fundamental operations of functions: addition, subtraction, multiplication, and division.
Explanation of addition of functions with an example of 3 + 8 = 11.
Definition of the sum of functions f(x) + g(x).
Explanation of subtraction of functions with an example of 10 - 2 = 8.
Definition of the difference of functions f(x) - g(x).
Explanation of multiplication of functions with an example of 3 * 5 = 15.
Definition of the product of functions f(x) * g(x).
Explanation of division of functions with an example of 16 / 2 = 8 and the importance of g(x) ≠ 0.
Definition of the quotient of functions f(x) / g(x) with the condition g(x) ≠ 0.
Example of applying the four operations to functions f(x) = x - 3 and g(x) = x + 5.
Calculation of f(x) + g(x) resulting in 2x + 2 and simplification to 2(x + 1).
Calculation of f(x) - g(x) resulting in -8 after simplification.
Application of the FOIL method to multiply (x - 3) and (x + 5).
Result of the multiplication (x - 3)(x + 5) leading to x^2 - 3x + 5x - 15.
Explanation of why division of binomials (x - 3) / (x + 5) cannot be simplified.
Conclusion of the lesson and a teaser for the next lesson on more complex operations.
Transcripts
good evening everyone
this is teacher sp and welcome back to
my channel
sucking channel mug subscribe like
comment and hit the notification bell so
that you will be updated for whatever
videos i'm going to upload
so you guys
i what we call operations of functions
how to evaluate the function right
and for fundamental operation now
function
we know that there are four fundamental
operations of functions
and these are addition subtraction
multiplication and division now
let us proceed to the concept of this
four
fundamental operation so like for
example
if i will be giving three plus
eight then the answer is equal to eleven
so this is what we call addition what do
you call
three and eight so we call this
our add-ins okay
so 3 and 8 and this 11
is what we call the sum so therefore
the sum of f
of x and g of x
is defined as f
of x plus g
of x so this is now
the formula for the operation addition
of function
how about this 10 minus 2
so we know that 10 minus 2 is equal to 8
so let us identify
10 is what we call the min win and 2
is what we call the subtrohen and what
do you call 8
8 is what we call the difference so
therefore
f of x and g of
x is defined as okay
the difference of f of x
minus g of x
okay and let us proceed now to number
three
three times five that is equal to
15. so what do you call three and
five so three and five are what we call
the factors
and is what we call the product
so therefore the product
of f of x and g of x
is defined as f of x
times g of x
okay but how about this one 16
divided by two is equal to eight
16 is what we call the dividend
2 is what we call the divisor and 8 is
what we call the quotient
so therefore the quotient of
f of x and g of x
is defined as f of
x over g
of x such that
g of x is not equal to
zero why bakit na ang atting g
of x is not equal to zero guys because
say
kappa zero and denominator mo the answer
is what we call undefined okay let us
prove for example
eight over
zero is undefined okay if your answer is
zero
zero times zero is equal to zero so we
know that this is
eight capacitor
so therefore all the numbers that the
denominator is
zero that is what we call the undefined
so these
are now the four operations the formula
of the four operations of functions okay
i will be giving you an example and we
will be using
this for operations
okay for example find
the value of
f of x is equal to x
minus 3 g of x
is equal to x plus 5
using the four operations of functions
so therefore
so using f of x plus g
of x so x
minus 3 x plus 5
then negative 3 and positive 5
that is equal to positive 2 x
and x so one plus one that is equal to
two x
plus two is this now our final answer
hindi fatto final answer nothing guys
we are going to get the common factor of
this
so therefore the common factor is 2
okay 2x divided by 2 that is equal to x
plus 2 divided by 2 is equal to 1.
so therefore the final answer is 2
times the quantity of x plus 1
okay now next is we are going to
subtract
x minus 3 and x
plus 5 so in subtracting this number
guys
so we have to follow the rule in
subtracting an
integer so the rule says that you are
going to change
the sign of the subtrahend and we know
that x plus 5 is the subtrahend
so therefore positive by gigi negative
positive becomes negative so negative 3
and negative 5 that is equal to negative
8
and positive x and negative x cancel ion
so therefore
the answer is equal to negative eight
okay so how about number three
okay number three is what we call
multiplication so we are going to
multiply
these two binomials x minus 3
and x plus 5 using
a foil method right so x times x that is
equal to
x squared negative 3
times x is equal to negative 3x
outer term is x times 5 that is equal to
5x
combine it together that will be equal
to
positive 2x okay
negative 3 times positive 5
is equal to negative 15. so therefore
this is now
the answer for the multiplication this
is now the product okay now let us
proceed letter
d which is the division so x
minus three okay divided by
x plus five you cannot divide this two
they are binomials you cannot also
use the cancellation method so therefore
this is now the answer using
the four fundamental operations of
functions
so i hope that uh you uh learn something
today
and for the next lesson we will be
proceeding or i will be explaining
the four fundamental operations but it's
a complicated
equation so thank you so much guys
and have a great day everyone
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