The function h(x)= (x + 6)^5 can be expressed in the form f(g(x)) where f ( x ) = x^5, and g(x) is defined below

Question

g(x)=

could someone help me with this? Thank you

Answer 1

We are given that h(x) = (x+6)⁵ and f(x) = x⁵.

We know that f(g(x)) = h(x).

Then, we need to find the function g(x) such that f(g(x)) = h(x) = (x+6)⁵.

In other words, we need to substitute a function g(x) into f(x) in order to get h(x).

But the only function that satisfies this relationship is g(x) = x+6.

Therefore, g(x) = x+6.

Answer 2

h(x) = f(g(x)) = (x + 6)⁵

Let f(x) = x⁵. Then g(x) will have to be x + 6.

Therefore, f(g(x)) = f(x + 6) = (x + 6)⁵.

Answer 3

Hello Lauren, h(x) does two things: adds 5 and then does the 6th power. What if f and g share these actions?

Since it says f(g(x)), the g(x) is inside so it goes first and f(x) goes second. They tell you that f(x) is doing the 5th power. What does g(x) have to do? Now write the formula for g(x). Tom S.