Answer
False
Work Step by Step
This statement is false. How do we know? Let $f$ be an invertible function such that $f(2) = 2$. Let's assume that $f^{-1}(2)=1/2$. The value of $f^{-1}(2)$ is the input to the function $f$ that produces an output of $2$.
Since $f$ is invertible, we know that $f(f^{-1}(x)) = x$ for all $x$ in the domain of $f$. Therefore, $f(f^{-1}(2)) =2$, which means $f(1/2) = 2$.
We got that to the value $y=2$ in the range of $f$ correspond two values of $x$ in the domain of $f$:
$f(2)=f(1/2)=2$
This contradicts the fact that the function is one to one. So our assumption that $f^{-1}(2)=1/2$ is wrong.
So, the correct statement is that $f^{-1}(2) = 2$, not $\frac{1}{2}$.
Therefore, the statement "If $f$ is an invertible function such that $f(2) = 2$, then $f ^{−1}(2) = 1/2$" is false.
