Question

Let f(x) = -2x^2– 7 and g(x) = 4x – 7.(fog)(x) =(gof)(x) =(fog)(1) =

Answer 1

Part 1.

The compositon fog is given by

$(f\circ g)(x)=-2(4x-7)^2-7$

which gives

$\begin{gathered} (f\circ g)(x)=-2(16x^2-56x+49)^{}-7 \\ (f\circ g)(x)=-32x^2+112x-98^{}-7 \\ (f\circ g)(x)=-32x^2+112x-105 \end{gathered}$

Then, the answer is:

$(f\circ g)(x)=-32x^2+112x-105$

Part 2.

The composition gof is given by

$(g\circ f)(x)=4(-2x^2-7)-7$

Then, the answer is:

$(g\circ f)(x)=-8x^2-35$

Part 3.

In this case, we need to substitute x=1 into the answer of Part 1, that is,

$\begin{gathered} (f\circ g)(1)=-32(1)^2+112(1)-105 \\ (f\circ g)(1)=-32^{}+112-105 \end{gathered}$

Therefore, the answer is:

$(f\circ g)(1)=-25$