How can I multiply this function?

Question

My function that are given are f(x-1)=3x-1 and g(x)=2x+5 and I don't know how to turn them into functions as f(x) and g(x), because I have to find (f*g)(x).

Answer 1

Given functions are f(x - 1) = 3x - 1 and g(x) = 2x + 5.

f(x - 1) = 3x - 1.

Replace x with (x + 1).

f[(x + 1) - 1] = 3(x + 1) - 1

f(x) = 3x + 3 - 1

f(x) = 3x + 2.

To find (f * g)(x) = f(x) * g(x)

                         = (3x + 2) * (2x + 5)

                         = (3x + 2)(2x) + (3x + 2)5

                         = 6x^2 + 4x + 15x +10

                         = 6x^2 + 19x + 10.

Therefore, (f * g)(x) = 6x^2 + 19x + 10.