1. Here the question is either
a: f(x-1)=[tex]- \frac{3}{4}x+2 [/tex], what is f(x)?
or
b) f(1-x)=[tex]- \frac{3}{4}x+2 [/tex], what is f(x)?
Case a: f(x-1)=[tex]- \frac{3}{4}x+2 [/tex], 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)=[tex]- \frac{3}{4}(x+1)+2[/tex]
f(x+1-1)=[tex]- \frac{3}{4}x- \frac{3}{4}+2[/tex]
f(x)=[tex]- \frac{3}{4}x- \frac{3}{4}+ \frac{8}{4}= - \frac{3}{4}x+\frac{5}{4}[/tex]
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)
