Question

Given f-1(x)=-3/4x+2 which equation represents f(x)

Answer 1

1. Here the question is either

a: f(x-1)=$- \frac{3}{4}x+2$, what is f(x)?
or
b) f(1-x)=$- \frac{3}{4}x+2$, what is f(x)?

Case a: f(x-1)=$- \frac{3}{4}x+2$, what is f(x)?

substitute x with x+1 in both sides. The reason is to get rid of 1 in the f() expression:

f((x+1)-1)=$- \frac{3}{4}(x+1)+2$

f(x+1-1)=$- \frac{3}{4}x- \frac{3}{4}+2$

f(x)=$- \frac{3}{4}x- \frac{3}{4}+ \frac{8}{4}= - \frac{3}{4}x+\frac{5}{4}$

b) in case b substitute x with (1-x) in both sides so that we get:
f(1-x)=f(1-(1-x))=f(1-1+x)=f(x)