Mathematics

Problem

Which statement about the graphs of a function

f

and its inverse

f^{-1}

is correct? a) The graph of

f^{-1}

is the reflection of the graph of

f

in the

y

-axis b) The graph of

f^{-1}

is the reflection of the graph of

f

in the line

y = x

c) The graph of

f^{-1}

is the reflection of the graph of

f

in the

x

-axis d) The graph of

f^{-1}

is obtained by rotating the graph of

f

90^{\circ}

about the origin

Intuitive explanation

The key insight is that $f$ and $f^{-1}$ are reflections of each other across the line $y = x$ . This means if a point $(a, b)$ lies on the graph of $f$ , then the point $(b, a)$ lies on the graph of $f^{-1}$ —the coordinates swap. Understanding this symmetry lets you quickly check which statement is true: look for relationships about mirroring, slopes, or how the graphs relate to that diagonal line.

Intuitive explanation

Browse the problem library