Reversing a one–one mapping

A many–one function has no inverse function on its stated domain: reversing its mapping gives two outputs for one input. Restrict the domain to a one–one branch first. To find an inverse, write y=f(x), solve for x, then interchange the variables. The inverse domain is the original range; its range is the original domain. f-1(x) is not 1f(x). For f(x)=x2, x 0, the inverse is sqrt(x), x 0. The points (2,4) and (4,2) are reflected in y=x. Choosing x 0 instead gives the negative square-root branch.