document.write( "Question 126726: Hi
\n" ); document.write( "could you help me with this?\r
\n" ); document.write( "\n" ); document.write( "Find the inverse of y=sqrtx+9. Is the inverse a function?\r
\n" ); document.write( "\n" ); document.write( "Thank you \n" ); document.write( "

Algebra.Com's Answer #92847 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Find the inverse of:
\n" ); document.write( " $\"y+=+sqrt%28x%29%2B9\"$ This could be written as: $\"f%28x%29+=+sqrt%28x%29%2B9\"$
\n" ); document.write( "To find the inverse of a function, interchange the x and y and solve for y.
\n" ); document.write( " $\"x+=+sqrt%28y%29%2B9\"$ Now solve for y by subtracting 9 from both sides.
\n" ); document.write( " $\"x-9+=+sqrt%28y%29\"$ Square both sides.
\n" ); document.write( " $\"%28x-9%29%5E2+=+y\"$ Simplify.
\n" ); document.write( " $\"y+=+x%5E2-18x%2B81\"$ Now replace the y with $\"f%5E%28-1%29%28x%29\"$ :
\n" ); document.write( " $\"f%5E%28-1%29%28x%29+=+x%5E2-18x%2B81\"$ This is the inverse function of $\"f%28x%29+=+sqrt%28x%29%2B9\"$ . And...yes, the inverse is a function!
\n" ); document.write( "To verify this, use the following rule: $\"f%28f%5E%28-1%29%28x%29%29+=+x\"$
\n" ); document.write( "In this case:
\n" ); document.write( " $\"f%28f%5E%28-1%29%28x%29%29+=+f%28x%5E2-18x%2B81%29\"$ Replace every x with $\"sqrt%28x%29%2B9\"$ and simplify:
\n" ); document.write( " $\"highlight%28%28sqrt%28x%29%2B9%29%5E2%29-highlight%2818%28sqrt%28x%29%2B9%29%29%2B81\"$ Simplify.
\n" ); document.write( " $\"highlight%28x%2B18sqrt%28x%29%2B81%29-highlight%2818sqrt%28x%29-162%29%2B81\"$ Combine like-terms.
\n" ); document.write( " $\"x%2Bhighlight%2818sqrt%28x%29-18sqrt%28x%29%29%2Bhighlight%2881-162%2B81%29\"$ = $\"x\"$ \n" ); document.write( "

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