Question

If g(x) = 2x + 2 and h(x) = 4x2 + 8x + 8, find a function f such that f ∘ g = h. (Think about what operations you would have to perform on the formula for g to end up with the formula for h.)

Answer 1

Answer:

Step-by-step explanation:

Hello,

$(\forall x \in \mathbb{R}) (fog)(x)=f(g(x))=f(2x+2)=h(x)=4x^2+8x+8\\\\=(2x+2)^2-2^2+4(2x+2)\\\\=(2x+2)^2+4(2x+2)-4\\\\\text{So, we conclude by.}\\\\\large \boxed{\sf \bf f(x)=x^2+4x-4}$