Chapter 0 - Before Calculus - 0.4 Inverse Functions - Exercises Set 0.4 - Page 45: 14

$\ f^{-1}(x)=\sqrt{\frac{5-x}{x}}\\$

$\ We\ are\ given\ that\ f(x)=\frac{5}{x^{2}+1}\\ \ Put\ y=\frac{5}{x^{2}+1}\\ \ Simplifying\ we\ get\ x^{2}+1=\frac{5}{y}\\ \ We\ get\ x^{2}=\frac{5}{y}-1\\ \ We\ get\ x^{2}=\frac{5-y}{y}\\ \ x=\sqrt{\frac{5-y}{y}}\\ \ Interchanging\ the\ values\ of\ x\ and\ y\ we\ get\ y=\sqrt{\frac{5-x}{x}}\\ \ Therefore\ f^{-1}(x)=\sqrt{\frac{5-x}{x}}\\$