Composición de funciones (Método fácil) gof(5)

Summary

In this video, the presenter explains how to calculate the composition of two functions and evaluate it at a specific point. The functions discussed are f(x) = √(2x² + 3x) and g(x) = x² + 8. The video guides viewers through the steps of computing g(f(x)) and evaluating it at x = 5. Key concepts like function composition, the use of absolute value when canceling a square with a square root, and proper substitution are covered in detail. The video concludes with a step-by-step breakdown of the calculations, resulting in the final answer of g(f(5)) = 73.

Takeaways

• 😀 The video explains how to calculate the composition of two functions, G and F.
• 😀 The functions given are F(x) = √(2x² + 3x) and G(x) = x² + 8.
• 😀 To calculate the composition, G ∘ F(x), the first step is to replace 'x' in G(x) with the expression for F(x).
• 😀 G ∘ F(x) = G( √(2x² + 3x) ) is formed by substituting F(x) into G(x).
• 😀 The process of simplifying involves canceling the square with the square root, which should be done carefully using absolute value to avoid negative results.
• 😀 The absolute value is important when simplifying a square root, as it ensures the result is always positive.
• 😀 After simplifying, the formula for G ∘ F(x) becomes |2x² + 3x| + 8.
• 😀 To evaluate the composition at x = 5, substitute 5 for x in the expression.
• 😀 The step-by-step calculation involves first squaring 5, multiplying by constants, and simplifying the result inside the absolute value.
• 😀 After performing the arithmetic, the final answer for G ∘ F(5) is 73.
• 😀 The video concludes with a call to action, encouraging viewers to like, subscribe, and share the video, while also inviting questions and suggestions in the comments.

Q & A

What is the purpose of the video?

The purpose of the video is to demonstrate how to calculate the composition of two functions and evaluate it at a specific point.

What are the two functions used in the video?

The two functions are F(x) = √(2x² + 3x) and G(x) = x³ + 8.

How is the composition of functions G and F represented?

The composition of functions G and F is represented as G(F(x)). In the video, this means substituting the function F(x) into the function G.

What is the first step to calculate G composition F of x?

The first step is to write the function G(x) and replace the x with parentheses. Then, inside those parentheses, we place the function F(x).

Why is it important to use absolute value when simplifying the composition of G and F?

It is important to use absolute value because when canceling a square with a square root, the result is the absolute value of the expression inside the square root. This ensures the result is non-negative, as the square root of any number is always non-negative.

How is the composition G(F(x)) simplified?

After substituting F(x) into G(x), the expression simplifies to the absolute value of (2x² + 3x) + 8.

What value is substituted for x when evaluating the composition at x = 5?

The value substituted for x is 5.

What are the first steps in evaluating G composition F at x = 5?

First, we substitute x = 5 into the composition expression. This involves calculating 2 * 5², 3 * 5, and then performing the necessary additions.

What is the result of the expression after substituting x = 5?

After substituting x = 5, we get the expression |65 + 8|, which simplifies to |73|. The result is 73.

What final value does G composition F of 5 equal?

The final value of G composition F at x = 5 is 73.