document.write( "Question 164342: Given f(x)=-2x+3, determine f^-1(x) \n" ); document.write( "

Algebra.Com's Answer #121065 by Earlsdon(6294) $\"\"$ $\"About$

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Given: $\"f%28x%29+=+-2x%2B3\"$ find the inverse $\"f%5E%28-1%29%28x%29\"$
\n" ); document.write( " $\"f%28x%29+=+-2x%2B3\"$ First, replace the f(x) with y to get:
\n" ); document.write( " $\"y+=+-2x%2B3\"$ Now exchange the x and y to get:
\n" ); document.write( " $\"x+=+-2y%2B3\"$ Now solve this for y by subtracting 3 from both sides.
\n" ); document.write( " $\"x-3+=+-2y\"$ Divide both sides by -2.
\n" ); document.write( " $\"%28x-3%29%2F-2+=+y\"$ Now replace the y with $\"f%5E%28-1%29%28x%29\"$ to get:
\n" ); document.write( " $\"highlight%28f%5E%28-1%29%28x%29+=+-%28x-3%29%2F2%29\"$
\n" ); document.write( "Check:
\n" ); document.write( " $\"f%28f%5E%28-1%29%28x%29%29+=+-2%28-%28x-3%29%2F2%29%2B3\"$
\n" ); document.write( " $\"f%28f%5E%28-1%29%28x%29%29+=+%28x-3%29%2B3\"$
\n" ); document.write( " $\"f%28f%5E%28-1%29%28x%29%29+=+x\"$ \r
\n" ); document.write( "
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