$f(x+1)= {3x+5 \over 2x+1}, x\neq-1/2, f(x)=?$

Question

$f(x+1)= {3x+5 \over 2x+1}, x\neq-1/2$

How can I get f(x)?

More generally, if I have $f(x+k)$ what do I have to do to get $f(x)$

Answer 1

You can get it easily applying the equality with $x-1$.

$$ f(x)=f((x-1)+1) = \dfrac{3(x-1)+6}{2(x-1)+1} $$

More generally,

$$ f(x) = f((x-k)+k) $$