document.write( "Question 60237: Find the inverse function of f. State the domain and range of f.
\n" ); document.write( "f(x) = (3x-2)/(x+5) \n" ); document.write( "

Algebra.Com's Answer #41423 by funmath(2933) $\"\"$ $\"About$

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Find the inverse function of f. State the domain and range of f.
\n" ); document.write( " $\"f%28x%29=%283x-2%29%2F%28x%2B5%29\"$ The demoninator cannot = 0, so x+5 cannot =0, x cannot =-5. Therefore the domain is that x is all real numbers except -5.
\n" ); document.write( "To find the inverse, let f(x)=y
\n" ); document.write( " $\"y=%283x-2%29%2F%28x%2B5%29\"$ Now switch your x and y and solve for y.
\n" ); document.write( " $\"x=%283y-2%29%2F%28y%2B5%29\"$
\n" ); document.write( " $\"x%28y%2B5%29=%283y-2%29%28y%2B5%29%2F%28y%2B5%29\"$
\n" ); document.write( " $\"xy%2B5x=%283y-2%29%2Across%28y%2B5%29%2Fcross%28y%2B5%29\"$
\n" ); document.write( " $\"xy%2B5x=3y-2\"$
\n" ); document.write( " $\"xy-3y%2B5x=3y-3y-2\"$
\n" ); document.write( " $\"xy-3y%2B5x-5x=-5x-2\"$
\n" ); document.write( " $\"y%28x-3%29=-5x-2\"$
\n" ); document.write( " $\"y%28x-3%29%2F%28x-3%29=%28-5x-2%29%2F%28x-3%29\"$
\n" ); document.write( " $\"y%2Across%28x-3%29%2Fcross%28x-3%29=%28-5x-2%29%2F%28x-3%29\"$
\n" ); document.write( " $\"y=%28-5x-2%29%2F%28x-3%29\"$
\n" ); document.write( "f^(-1)(x)= $\"%28-5x-2%29%2F%28x-3%29\"$ <-- this is the inverse function.
\n" ); document.write( "The range is anything that doesn't make the inverse undefined: y can be all real numbers except y cannot = 3.
\n" ); document.write( "Happy Calculating!!! \n" ); document.write( "

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