document.write( "Question 1149980: Given f(x) below, find f^-1(x). \r
\n" ); document.write( "\n" ); document.write( "F(x)=-3x+1/x-5 X=/ 5
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Algebra.Com's Answer #771325 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "Use parentheses!

\n" ); document.write( "The function you show, y = -3x+1/x-5, is $\"y+=+-3x%2B1%2Fx-5\"$ -- clearly not what you want.

\n" ); document.write( "The function you want is y = (-3x+1)/(x-5), which is $\"y+=+%28-3x%2B1%29%2F%28x-5%29\"$

\n" ); document.write( "One standard way of finding the inverse of a given function is to switch the x and y and solve for the new y:

\n" ); document.write( " $\"x+=+%28-3y%2B1%29%2F%28y-5%29\"$
\n" ); document.write( " $\"x%28y-5%29+=+-3y%2B1\"$
\n" ); document.write( " $\"xy-5x+=+-3y%2B1\"$
\n" ); document.write( " $\"xy%2B3y+=+5x%2B1\"$ [gather all the terms with y on one side]
\n" ); document.write( " $\"y%28x%2B3%29+=+5x%2B1\"$
\n" ); document.write( " $\"y+=+%285x%2B1%29%2F%28x%2B3%29\"$

\n" ); document.write( "The inverse is

\n" ); document.write( " $\"%285x%2B1%29%2F%28x%2B3%29\"$

\n" ); document.write( "If you see problems like this often involving inverses of functions like this, note there is a pattern you can use to write the inverse without going through the algebra to find it.

\n" ); document.write( "Look at the original function and it inverse:

\n" ); document.write( " $\"%28-3x%2B1%29%2F%28x-5%29\"$ and $\"%285x%2B1%29%2F%28x%2B3%29\"$

\n" ); document.write( "The coefficient of x in the numerator and the constant in the denominator switch places and change sign; the constant in the numerator and the coefficient of x in the denominator remain unchanged.

\n" ); document.write( "In general, the inverse of $\"%28ax%2Bb%29%2F%28cx%2Bd%29\"$ is $\"%28-dx%2Bb%29%2F%28cx-a%29\"$

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