Question

f(x)= sqare root x-5. find f^1

Answer 1

$f(x)=\sqrt{x-5}\\The\ domain\ D_f=x-5\geq0\to x\geq5\\\\y=\sqrt{x-5}\ \ \ \ |square\ both\ sides\\\\y^2=x-5\ \ \  \ \ |add\ 5\ to\ both\ sides\\\\x=y^2+5\\\\Answer:\boxed{f^{-1}(x)=x^2+5\ for\ x\in[0;\ \infty)}$