Question

show that f o f^-1(x) = x for y = mx+c

Answer 1

\[f\circ f^{-1}(x)=x\] by definition of
\[f^{-1}\]

Answer 2

but i guess in your case you are supposed to find
\[f^{-1}(x)\] and then check

Answer 3

\[y = mx+b\] solve for x get
\[x=\frac{y-b}{m}\] and so
\[f^{-1}(x)=\frac{x-b}{m}\] and now we can check directly that
\[f\circ f^{-1}(x)=x\]

Answer 4

\[f\ circ f^{-1}(x)=f(f^{-1}(x))=f(\frac{x-b}{m})=m\frac{x-b}{m} +b\] and you are done in one algebra step