Question

In the following problem, verify that f(f^-1(x))=x and that f^-1 (f(x))= x

Answer 1

\[f (x)= \left(\begin{matrix}6x-7 \\ 2-x\end{matrix}\right)\]

Answer 2

and \[f^(-1) (x)= \left(\begin{matrix}2x+7 \\ 6+x\end{matrix}\right)\]

Answer 3

f(x) wants a value x as input. Above, you've said you want that input to be f^-1(x). So, in f(x)=(6x-7)/(2-x) replace x with f^-1(x) = (2x+7)/(6+x). See what you get... shoudl come out as x. Now do similar by the other way...

Answer 4

\[f(x)=\frac{6x-7}{2-x}\]
\[f^{-1}(x)=\frac{2x+7}{6+x}\]
\[f\circ f^{-1}(x)=f(f^{-1}(x))=\]
\[=\frac{6\times (\frac{2x+7}{x+6})-7}{2-(\frac{2x+7}{6+x})}\]

Answer 5

Thanks