Question 1157688
If {{{sqrt(x-1)}}} and {{{x^2+1}}} are inverses, than f(g(x))=x and g(f(x))=x {{{g(f(x))=g(sqrt(x-1))=(sqrt(x-1))^2+1=x-1+1=x}}}. {{{f(g(x))=f(x^2+1)=sqrt(x^2+1-1)=sqrt(x^2)}}}, which does <b>not</b> equal x. It equals {{{abs(x)}}}, not x. Therefore, f(x) and g(x) are not inverses. However, if you restrict the domain of g to {{{x>=0}}}, <b><u><i>then</i></u></b> f and g are inverses.