document.write( "Question 1061291: One-to-one function is h(x)=8x-3/3x+5. Find h^-1(x), where h^-1 is the inverse of h. Also state domain and range of h^-1 in interval notation.
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Algebra.Com's Answer #676199 by Fombitz(32388) $\"\"$ $\"About$

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Use x,y nomenclature.
\n" ); document.write( " $\"y=%288x-3%29%2F%283x%2B5%29\"$
\n" ); document.write( "Interchange x and y,
\n" ); document.write( " $\"x=%288y-3%29%2F%283y%2B5%29\"$
\n" ); document.write( " $\"%283y%2B5%29x=8y-3\"$
\n" ); document.write( " $\"3xy%2B5x=8y-3\"$
\n" ); document.write( " $\"3xy-8y=-3-5x\"$
\n" ); document.write( " $\"%283x-8%29y=-3-5x\"$
\n" ); document.write( " $\"y=%283%2B5x%29%2F%288-3x%29\"$
\n" ); document.write( " $\"h%5E%28-1%29%28x%29=%283%2B5x%29%2F%288-3x%29\"$
\n" ); document.write( "Domain is all x except,
\n" ); document.write( " $\"8-3x=0\"$
\n" ); document.write( " $\"8=3x\"$
\n" ); document.write( " $\"x=8%2F3\"$
\n" ); document.write( "Determine the range from the domain of the original function,
\n" ); document.write( " $\"3x%2B5=0\"$
\n" ); document.write( " $\"3x=-5\"$
\n" ); document.write( " $\"x=-5%2F3\"$
\n" ); document.write( "Since $\"x=-5%2F3\"$ is excluded from h domain, it is also excluded from the inverse's range. \n" ); document.write( "

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