Determine whether the statement is true or false.
-If f is a one-to-one function and the graph of f lies completely within the first and fourth quadrants, then the
graph of $\mathrm { f } ^ { - 1 }$ lies completely within the first and second quadrants.

Question

Quizplus · Accepted Answer

If $f$ is a one-to-one function and its graph lies in the first and fourth quadrants, it means $f$ only takes positive values for $y$ when $x$ is positive (first quadrant) and negative values for $y$ when $x$ is negative (fourth quadrant). Since the inverse function $f^{-1}$ essentially swaps the roles of $x$ and $y$, the graph of $f^{-1}$ will lie in the first quadrant (where both $x$ and $y$ are positive, corresponding to the positive $y$ values of $f$ for positive $x$) and the second quadrant (where $x$ is negative and $y$ is positive, corresponding to the negative $x$ values of $f$ for negative $y$).

Determine Whether the Statement Is True or False f−1\mathrm { f } ^ { - 1 }f−1

Determine Whether the Statement Is True or False $\mathrm { f } ^ { - 1 }$