\( \def\dfrac#1#2{\displaystyle\frac{#1}{#2}} \def\solve#1{\begin{array}{rcl}#1\end{array} } \)

Home / 01 Mathematical Functions / 28 Inverse Functions Horizontal Line Test

The graph below represents a function with a domain of all real numbers, \(f(x) = x^2\). This function does not have an inverse function on this domain. Notice that for most horizontal lines, there are two possible paths back to the input space (one positive, one negative). This fails the horizontal line test and thus does not have an inverse function.