document.write( "Question 346009: find the inverse of following functions:
\n" ); document.write( "(a) f(x)=(x^3 + 5)/(x-3) , x≠3
\n" ); document.write( "
\n" ); document.write( "(b)f(x)=(x^3 - 8)/(x^2 - 4) , x≠ą2 \n" ); document.write( "

Algebra.Com's Answer #247445 by jsmallt9(3758) $\"\"$ $\"About$

You can put this solution on YOUR website!
To find inverses:

Replace the function notation, if any, with a \"y\".
Rewrite the equation writing an \"x\" where you have a \"y\" and writing a \"y\" where you have a \"x\". This step is where you are changing the function to its inverse.
If possible, solve the resulting equation for y. If you are able to find a single expression for y, then the inverse of the function is a function, too.

\n" ); document.write( "Let's try this out:
\n" ); document.write( " $\"f%28x%29=%28x%5E3+%2B+5%29%2F%28x-3%29\"$
\n" ); document.write( "1) Replace function notation:
\n" ); document.write( " $\"y+=+%28x%5E3+%2B+5%29%2F%28x-3%29\"$
\n" ); document.write( "2) Swap the x's and y's:
\n" ); document.write( " $\"x+=+%28y%5E3+%2B+5%29%2F%28y-3%29\"$
\n" ); document.write( "This is the inverse relation.
\n" ); document.write( "3) Solve fo y, if possible.
\n" ); document.write( "Multiply both sides by y-3:
\n" ); document.write( " $\"xy+-+3x+=+y%5E3+%2B+5\"$
\n" ); document.write( "Gather the y terms on one side and everything else on the other side of the equation. I'm going to subtract xy and 5 from each side:
\n" ); document.write( " $\"-3x+-5+=+y%5E3+-xy\"$
\n" ); document.write( "At this point I don't see a way to solve for y. So the inverse is not a function.

\n" ); document.write( " $\"f%28x%29=%28x%5E3+-+8%29%2F%28x%5E2+-+4%29\"$
\n" ); document.write( "1) Replace function notation:
\n" ); document.write( " $\"y+=+%28x%5E3+-+8%29%2F%28x%5E2+-+4%29\"$
\n" ); document.write( "2) Swap the x's and y's:
\n" ); document.write( " $\"x+=+%28y%5E3+-+8%29%2F%28y%5E2+-+4%29\"$
\n" ); document.write( "This is the inverse relation.
\n" ); document.write( "3) Solve for y, if possible
\n" ); document.write( "Multiply both sides by $\"y%5E2+-+4\"$
\n" ); document.write( " $\"xy%5E2+-+4x+=+y%5E3+-+8\"$
\n" ); document.write( "Gather the y terms on one side:
\n" ); document.write( " $\"-4x+%2B+8+=+y%5E3+-xy%5E2\"$
\n" ); document.write( "And again I don't see a way to solve for y. So this inverse in not a finction either. \n" ); document.write( "

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