How do you solve this homework problem?

Question

[f times g](x)

f(x)= x 1

g(x)= 3x-4

Steps please, thanks!

Answer 1

Did you want fg with a tiny dot meaning in f times g, or did you want f o g with a larger circle meaning f composed with g?  

f times g =

(fg)(x) =

(x + 1)(3x - 4) =

(x)(3x) + (x)(-4) + (1)(3x) + (1)(-4) =

3x² - 4x + 3x - 4 =

3x² - x - 4

f composed with g =

(fog)(x) =

f(g(x)) =

f(3x - 4) =

(3x - 4) + 1 =

3x - 4 + 1 =

3x - 3

Hope this helps you!