Question

The function h(x)=(x+2)^8 can be expressed in the form f(g(x)), where f(x)=x^8, and g(x) is defined below:

g(x)=

Answer 1

[AI-generated answer — Bot GPT 3.5]

x+2

Answer 2

[AI-generated answer — Step-by-Step Bot]

g(x) = x + 2

Answer 3

[AI-generated answer — Explain Bot]

To determine the expression for g(x), we need to think about what transformation is happening to x in the function h(x)=(x+2)^8.

In h(x), we can see that x is being shifted to the left by 2 units, and then raised to the power of 8. Therefore, g(x) will involve the transformation of shifting x to the left by 2 units.

To express this mathematically, we need to define g(x) as x shifted to the left by 2 units. We can do this by subtracting 2 from x. Therefore, the expression for g(x) is:

g(x) = x - 2

Now, if we substitute g(x) into the function f(x)=(x+2)^8, we get:

f(g(x)) = (g(x) + 2)^8 = ((x - 2) + 2)^8 = x^8

So, the function h(x) = (x+2)^8 can indeed be expressed in the form f(g(x)), where f(x) = x^8 and g(x) = x - 2.