For f(x) = 3x + 1 and g(x) = x^(2) - 6, find (f * g)(x) A. 3x^(2) - 17 B. 3x^(3) + x^(2) - 6x -6 C. 4x^(2) -6x - 8 D. 3x^(3) + x^(2) - 18x -6

Question

For
`f(x) = 3x + 1` and
`g(x) = x^(2) - 6`, find
`(f * g)(x)`

A.
`3x^(2) - 17`
B.
`3x^(3) + x^(2) - 6x -6`
C.
`4x^(2) -6x - 8`
D.
`3x^(3) + x^(2) - 18x -6`

Answer 1

`3x^3+x^2-18x-6`

Explanation:

f(x)= 3x+1 and g(x)= x^2 - 6

we need to find (f*g)(x)

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

Plug in the given f(x) and g(x)

`(f*g)(x)= f(x) * g(x)= (3x+1)(x^2-6)`

Apply FOIL method to multiply it

`(3x+1)(x^2-6)= 3x^3 -18x+x^2-6= 3x^3+x^2-18x-6`