document.write( "Question 1095376: Functions f and g are defined by f : x tends to
\n" ); document.write( "x/(x-3) , x not equals 3, g : x tends to 3x+5. Find the value of x for which (f . g )^-1 (x) = 5/3. \n" ); document.write( "

Algebra.Com's Answer #709937 by greenestamps(13200) $\"\"$ $\"About$

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I will assume that by \"(f.g)^-1(x)\" you mean the inverse of the composition of functions f and g; that is,
\n" ); document.write( " $\"%28%28f%28g%28x%29%29%29%5E-1%29\"$

\n" ); document.write( "In that case, the problem is asking you to find the input value x for which
\n" ); document.write( " $\"f%28g%28x%29%29+=+5%2F3\"$

\n" ); document.write( "Then
\n" ); document.write( " $\"f%28g%28x%29%29+=+%283x%2B5%29%2F%28%283x%2B5%29-3%29+=+%283x%2B5%29%2F%283x%2B2%29\"$
\n" ); document.write( "so
\n" ); document.write( " $\"%283x%2B5%29%2F%283x%2B2%29+=+5%2F3\"$
\n" ); document.write( " $\"9x%2B15+=+15x%2B10\"$
\n" ); document.write( " $\"5+=+6x\"$
\n" ); document.write( " $\"x+=+5%2F6\"$

\n" ); document.write( "Check:
\n" ); document.write( " $\"g%285%2F6%29+=+3%285%2F6%29%2B5+=+5%2F2%2B5+=+15%2F2\"$
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