document.write( "Question 54929: I have to find the inverse of g(x) = the square root of x -4 \r
\n" ); document.write( "\n" ); document.write( "In order to find the inverse you switch the x and y.\r
\n" ); document.write( "\n" ); document.write( "x = square root of y - 4\r
\n" ); document.write( "\n" ); document.write( "I have to get the y by itself, so I squared both sides, leaving me with:\r
\n" ); document.write( "\n" ); document.write( "x^2 = y - 4
\n" ); document.write( "x^2 + 4 = y \r
\n" ); document.write( "\n" ); document.write( "Is this the final answer? \n" ); document.write( "

Algebra.Com's Answer #37132 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Yes, you did it correctly, but you should finish the problem by replacing y with $\"g%5E%28-1%29%28x%29\"$ so you have:
\n" ); document.write( " $\"g%5E%28-1%29%28x%29+=+x%5E2%2B4\"$ \r
\n" ); document.write( "\n" ); document.write( "To check you solution, remember that:
\n" ); document.write( " $\"g%28g%5E%28-1%29%29%28x%29+=+x\"$ and $\"g%5E%28-1%29%28g%28x%29%29+=+x\"$ \r
\n" ); document.write( "\n" ); document.write( "Let's look at the first check: $\"g%28x%29+=+sqrt%28x-4%29\"$
\n" ); document.write( " $\"g%28g%5E%28-1%29%28x%29%29+=+x\"$
\n" ); document.write( " $\"g%28x%5E2%2B4%29+=+sqrt%28%28x%5E2%2B4%29-4%29\"$ Simplifying this, you get:
\n" ); document.write( " $\"sqrt%28x%5E2%29+=+x\"$ This checks out fine.\r
\n" ); document.write( "\n" ); document.write( "Now we'll do the second check:
\n" ); document.write( " $\"g%5E%28-1%29%28g%28x%29%29+=+x\"$
\n" ); document.write( " $\"g%5E%28-1%29%28sqrt%28x-4%29%29+=+sqrt%28%28x%5E2%2B4%29-4%29\"$ Simplifying this, you get:
\n" ); document.write( " $\"sqrt%28x%5E2%29+=+x\"$ This also checks. \n" ); document.write( "

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