document.write( "Question 1157688: show that f(x)=sqrt(x-1) and g(x)=x^2+1 are inverses \n" ); document.write( "

Algebra.Com's Answer #780603 by Shin123(626) $\"\"$ $\"About$

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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. \n" ); document.write( "

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