SOLUTION: show that f(x)=sqrt(x-1) and g(x)=x^2+1 are inverses

Algebra ->  Inverses -> SOLUTION: show that f(x)=sqrt(x-1) and g(x)=x^2+1 are inverses      Log On


   

Question 1157688: show that f(x)=sqrt(x-1) and g(x)=x^2+1 are inverses
Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
If sqrt%28x-1%29 and x%5E2%2B1 are inverses, than f(g(x))=x and g(f(x))=x g%28f%28x%29%29=g%28sqrt%28x-1%29%29=%28sqrt%28x-1%29%29%5E2%2B1=x-1%2B1=x. f%28g%28x%29%29=f%28x%5E2%2B1%29=sqrt%28x%5E2%2B1-1%29=sqrt%28x%5E2%29, which does not equal x. It equals abs%28x%29, not x. Therefore, f(x) and g(x) are not inverses. However, if you restrict the domain of g to x%3E=0, then f and g are inverses.