document.write( "Question 1061793: Please help me solve this equation: find the inverse of the function
\n" ); document.write( " $\"f%28x%29=x%5E2%2B1%2F2\"$ \n" ); document.write( "

Algebra.Com's Answer #676552 by KMST(5328) $\"\"$ $\"About$

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With the function $\"f%28x%29\"$ as written,
\n" ); document.write( "there is an inverse relation (not an inverse function),
\n" ); document.write( " $\"y+=%22+%22+%2B-+sqrt%28%282x-1%29%2F2%29\"$ ,
\n" ); document.write( "that can be found from $\"y=x%5E2%2B1%2F2\"$
\n" ); document.write( "by interchanging $\"x\"$ and $\"y\"$ ,
\n" ); document.write( "and then \"solving for y.\"
\n" ); document.write( "If we define the function with a restricted domain, as
\n" ); document.write( " $\"f%28x%29=x%5E2%2B1+%2F+2\"$ $\"%22+%2C%22\"$ $\"%22for%22\"$ $\"x%3E=0%29\"$ ,
\n" ); document.write( "then it has an inverse function, which is
\n" ); document.write( " $\"f%5E%28-1%29\"$ $\"%28x%29=sqrt%28%282x-1%29%2F2%29\"$ or $\"f%5E%28-1%29\"$ $\"%28x%29=sqrt%28x-1%2F2%29\"$ .
\n" ); document.write( "When we interchange $\"x\"$ and $\"y\"$ from $\"y=x%5E2%2B1%2F2\"$ $\"%22+%2C%22\"$ $\"%22for%22\"$ $\"x%3E=0%29\"$ ,
\n" ); document.write( "we get
\n" ); document.write( " $\"x=y%5E2%2B1%2F2\"$ $\"%22+%2C%22\"$ $\"%22with%22\"$ $\"y%3E=0%29\"$ ,
\n" ); document.write( " $\"x=%282y%5E2%2B1%29%2F2\"$ $\"%22+%2C%22\"$ $\"%22with%22\"$ $\"y%3E=0%29\"$ ,
\n" ); document.write( " $\"2x=2y%5E2%2B1\"$ $\"%22+%2C%22\"$ $\"%22with%22\"$ $\"y%3E=0%29\"$ ,
\n" ); document.write( " $\"2x-1=2y%5E2\"$ $\"%22+%2C%22\"$ $\"%22with%22\"$ $\"y%3E=0%29\"$ ,
\n" ); document.write( " $\"%282x-1%29%2F2=y%5E2\"$ $\"%22+%2C%22\"$ $\"%22with%22\"$ $\"y%3E=0%29\"$ , and
\n" ); document.write( " $\"y=sqrt%28%282x-1%29%2F2%29\"$ <--> $\"y=sqrt%28x-1%2F2%29\"$ . \n" ); document.write( "

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