Question

If f(g(x))=x and f(x) = 3x – 4, find g(x)

A. g(x)=(x-4)/3
B. g(x)=(x+4)/3
C. g(x)=(x/3)+4
D. g(x)=(x/3)-4

Answer 1

`f(g(x))=x;\ f(x)=3x-4\\\\therefore3[g(x)]-4=x\ \ \ |add\ 4\ to\ both\ sides\\\\3[g(x)]=x+4\ \ \ \ |divide\ both\ sides\ by\ 3\\\\g(x)=(x+4)/(3)\\\\Answer:\boxed{B.\ g(x)=(x+4)/(3)}`

Answer 2

we can do reverse engineering to identify the function or expression of g(x). we can try each function as g(x).

a. f(g(x)) = 3*( (x-4)/3) – 4 = x-4-4 = x -8
b. f(g(x)) = 3*( (x+4)/3) – 4 = x+ 4 -4 = x

Hence the answer should be B