Part 1.
The compositon fog is given by
[tex](f\circ g)(x)=-2(4x-7)^2-7[/tex]
which gives
[tex]\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}[/tex]
Then, the answer is:
[tex](f\circ g)(x)=-32x^2+112x-105[/tex]
Part 2.
The composition gof is given by
[tex](g\circ f)(x)=4(-2x^2-7)-7[/tex]
Then, the answer is:
[tex](g\circ f)(x)=-8x^2-35[/tex]
Part 3.
In this case, we need to substitute x=1 into the answer of Part 1, that is,
[tex]\begin{gathered} (f\circ g)(1)=-32(1)^2+112(1)-105 \\ (f\circ g)(1)=-32^{}+112-105 \end{gathered}[/tex]
Therefore, the answer is:
[tex](f\circ g)(1)=-25[/tex]
