Question

Let f(x) = 4x + 4 and g(x) = 5x2 - 4. Evaluate (fog)(2). (fog)(2)=(Simplify your answer.)

Answer 1

We know that

$f(x)=4x+4,g(x)=5x^2-4$

To find (fog)(2), we have to find first (fog)(x), which is the composition of g(x) inside f(x), as follows

$(f\circ g)(x)=f(g(x))=4(5x^2-4)+4=20x^2-16+4=20x^2-12$

Now, we evaluate the expression for x = 2

$(f\circ g)(2)=20(2)^2-12=20(4)-12=80-12=68$

Therefore, the composition (fog)(2) is equal to 68.