Question

F(x) = square root x - 5 find f^-1

Answer 1

as you may know, to get the "inverse relation" of any expression, we start off by doing a quick switcharoo on the variables, and then we solve for "y".


`\bf \stackrel{f(x)}{y}=√(x-5)\qquad \boxed{x}=\sqrt{\boxed{y}-5}\impliedby \textit{let's square both sides} \\\\\\ (x)^2=(√(y-5))^2\implies x^2=y-5\implies x^2+5=\stackrel{f^(-1)(x)}{y}`