Question

If h(x) = (fog)(x) and h(x) = 4(x+1)^2, find one possibility for f(x) and g(x).

Answer 1

Answer:

Option C

Step-by-step explanation:

We will check all the options one by one to see which group of function produces h(x)

Option A:

$f(x) = x+1\\g(x) = 4x^2\\(fog)(x) = g(x) + 1\\= 4x^2+1$

Not correct..

Option B:

$f(x) = 4x^2\\g(x)=(x+1)^2\\(fog)(x) = 4(g(x))^2\\= 4[(x+1)^2]^2$

Not Correct

Option C:

$f(x) = 4x^2\\g(x) = x+1\\(fog)(x) = 4(g(x))^2\\= 4(x+1)^2$

The composition is same as h(x) so it is the correct answer ..