Question

complete the following sentence. if (f^{-1}) denotes the inverse of a function (f), then the graphs of (f) and (f^{-1}) are symmetric with respect to the line (type an equation.)

Explanation:

The graphs of a function and its inverse are symmetric about the line $y = x$. This is a fundamental property in the study of inverse - functions. If $(a,b)$ is a point on the graph of $y = f(x)$, then $(b,a)$ is a point on the graph of $y = f^{-1}(x)$, and the line $y=x$ is the line of symmetry for these two points.

Answer:

$y = x$