Determine whether the statement is true or false.
-If $\mathrm { f }$ is a one-to-one function and the graph of $\mathrm { f }$ 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

Since $\mathrm { f }$ is one-to-one and its graph lies in the first and fourth quadrants, it means $\mathrm { f }$ only outputs positive values for positive inputs and negative values for negative inputs. The inverse function $\mathrm { f } ^ { - 1 }$ will then take these positive and negative values as its inputs, and output the corresponding positive x-values, placing its graph in the first and second quadrants.

Determine Whether the Statement Is True or False f\mathrm { f }f

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