Question

PLEASE HELP FOR MATH

Answer 1

`f(x) = 3x^2` and
`g(x) = x + 2`

Explanation:

Given

`h(x) = 3(x+2)^2`

`h(x) = (fog)(x)`

Required

Find possible expressions for f(x) and g(x)

`h(x) = (fog)(x)`

This can be rewritten as:

`h(x) = f(g(x))`

Recall that
`h(x) = 3(x+2)^2`

So;

`h(x) = f(g(x)) = 3(x+2)^2`

`f(g(x)) = 3(x+2)^2`

By comparison, the expression in bracket represents g(x);

Hence;

`g(x) = x + 2`

Replace g(x) with x

`f(x) = 3(x)^2`

`f(x) = 3x^2`

Hence, the possible expressions of f(x) and g(x) are:

`f(x) = 3x^2` and
`g(x) = x + 2`