Question

The function h(x) = (x +9) can be expressed in the form f(g(x)) where f(x) = x³, and g(x)

is defined below:
g(x)=

Answer 1

g(x) = x + 3

Explanation:

To see how this works, we can plug g(x) into f to get:

f(g(x)) = f(x + 3) = (x + 3)^3

Then, we can simplify h(x) = (x + 9) as follows:

h(x) = (x + 9) = ((x + 3) + 6) = g(x) + 6

Finally, we can write h(x) in terms of f(g(x)) as:

h(x) = g(x) + 6 = f(g(x)) + 6 = f(x + 3) + 6 = (x + 3)^3 + 6