For this case we have the following functions:
[tex]f (x) = x-7\\g (x) = x ^ 2 + 1[/tex]
We must find [tex](f * g) (x)[/tex]. By definition we have to:
[tex](f * g) (x) = f (x) * g (x)[/tex]
So:
[tex](f*g)(x)=(x-7)(x^2+1)[/tex]
We apply distributive property:
[tex](f * g) (x) = x ^ 3 + x-7x ^ 2-7\\(f * g) (x) = x ^ 3-7x ^ 2 + x-7[/tex]
We evaluate at [tex]x = -1:[/tex]
[tex](f * g) (- 1) = (- 1) ^ 3-7 (-1) ^ 2 + (- 1) -7\\(f * g) (- 1) = - 1-7 (1) -1-7\\(f * g) (- 1) = - 1-7-1-7[/tex]
Equal signs are added and the same sign is placed:
[tex](f * g) (- 1) = - 16[/tex]
Answer:
[tex](f * g) (- 1) = - 16[/tex]
