Answer
False statement
Work Step by Step
We have to check if the following statement is true:
"If $f$ is an even function, then $f^{-1}$ exists."
Consider the function:
$f(x)=x^2$
Check if the function is even:
$f(-x)=(-x)^2=x^2=f(x)\checkmark$
Graph the function and use the Horizontal Line Test. The test fails, so the function doesn't have an inverse.
This shows that the given statement is FALSE.
