Question

If f(x)=x^2+2x−5 and g(x)=2x+4, what is (f⋅g)(x)

Answer 1

Explanation:

f(x)=x²+2x−5 and g(x)=2x+4

(f⋅g)(x) = (x²+2x−5)(2x+4) = 2x^3 +4x² -10x +4x²+8x-20

(f⋅g)(x) = 2x^3+8x² -2x -20

Answer 2

For this case we have the following functions:

`f (x) = x ^ 2 + 2x-5\\g (x) = 2x + 4`

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

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

So:

`(f * g) (x) = (x ^ 2 + 2x-5) (2x + 4)`

Applying distributive property we have:

`(f * g) (x) = 2x ^ 3 + 4x ^ 2 + 4x ^ 2 + 8x-10x-20`

We add similar terms:

`(f * g) (x) = 2x ^ 3 + 8x ^ 2-2x-20`

Answer:

`(f * g) (x) = 2x ^ 3 + 8x ^ 2-2x-20`