Question

Given the functions f(x)=x-7 and g(x)=x^2+1, evaluate (f*g)(-1).

I keep getting -16, but that's not an answer choice...?

Answer 1

For this case we have the following functions:

`f (x) = x-7\\g (x) = x ^ 2 + 1`

We must find
`(f * g) (x)`. By definition we have to:

`(f * g) (x) = f (x) * g (x)`

So:

`(f*g)(x)=(x-7)(x^2+1)`

We apply distributive property:

`(f * g) (x) = x ^ 3 + x-7x ^ 2-7\\(f * g) (x) = x ^ 3-7x ^ 2 + x-7`

We evaluate at
`x = -1:`

`(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`

Equal signs are added and the same sign is placed:

`(f * g) (- 1) = - 16`

Answer:

`(f * g) (- 1) = - 16`