Answer
False.
Work Step by Step
We prove that this statement is false by giving a counter example.
Suppose $f(x) = 2x - 2$. The inverse of f is $f^{-1}(x) = \frac{1}{2}(x + 2)$.
Here, $f(2) = 2(2) - 2 = 2$
$f^{-1}(2) = \frac{1}{2}(2 + 2) = 2$
Thus, we prove that in general, the statement is not true. It may be true for some cases (say when $f(x) = x$) but it is definitely not true for all cases or functions. .
