document.write( "Question 205007: I need help with inverse problems. What is the inverse of the function f(x)=x+2/x-2? \n" ); document.write( "

Algebra.Com's Answer #154755 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Find the inverse of:
\n" ); document.write( " $\"f%28x%29+=+%28x%2B2%29%2F%28x-2%29\"$ First, substitute: $\"f%28x%29+=+y\"$
\n" ); document.write( " $\"y+=+%28x%2B2%29%2F%28x-2%29\"$ Now interchange the two variables, x and y.
\n" ); document.write( " $\"x+=+%28y%2B2%29%2F%28y-2%29\"$ Now solve this for y. Multiply both sides by (y-2).
\n" ); document.write( " $\"x%28y-2%29+=+y%2B2\"$ Expand the left side.
\n" ); document.write( " $\"xy-2x+=+y%2B2\"$ Add 2x to both sides.
\n" ); document.write( " $\"xy+=+2x%2By%2B2\"$ Now subtract y from both sides.
\n" ); document.write( " $\"xy-y+=+2x%2B2\"$ Factor the y on the left side.
\n" ); document.write( " $\"y%28x-1%29+=+2x%2B2\"$ finally, divide both sides by (x-1).
\n" ); document.write( " $\"y+=+%282x%2B2%29%2F%28x-1%29\"$ and now replace y with $\"f%5E-1%28x%29\"$ to get:
\n" ); document.write( " $\"highlight%28f%5E-1%28x%29+=+%282x%2B2%29%2F%28x-1%29%29\"$
\n" ); document.write( "Now if you want to prove the answer is correct, then you must show that:
\n" ); document.write( " $\"f%28f%5E-1%28x%29%29+=+x\"$
\n" ); document.write( " $\"f%28f%5E-1%28x%29%29+=+f%28%282x%2B2%29%2F%28x-1%29%29\"$
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Simplify.
\n" ); document.write( " $\"f%28f%5E-1%28x%29%29+=+%28%282x%2B2%29%2B2%28x-1%29%29%2F%28%282x%2B2%29-2%28x-1%29%29\"$
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Cancel the 2's and simplify.
\n" ); document.write( " $\"f%28f%5E-1%28x%29%29+=+2x%2F2\"$
\n" ); document.write( " $\"f%28f%5E-1%28x%29%29+=+x\"$ OK! \n" ); document.write( "

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