document.write( "Question 54968: Find the Inverse of the following function:\r
\n" ); document.write( "\n" ); document.write( "f(x)=10^(x-3)+4 \n" ); document.write( "

Algebra.Com's Answer #37161 by funmath(2933) $\"\"$ $\"About$

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Find the Inverse of the following function:
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\n" ); document.write( " $\"f%28x%29=10%5E%28x-3%29%2B4\"$
\n" ); document.write( " $\"y=10%5E%28x-3%29%2B4\"$ Switch the x and y and solve for y.
\n" ); document.write( " $\"x=10%5E%28y-3%29%2B4\"$
\n" ); document.write( " $\"x-4=10%5E%28y-3%29%2B4-4\"$
\n" ); document.write( " $\"x-4=10%5E%28y-3%29\"$ Take the log of both sides:
\n" ); document.write( " $\"log%28%28x-4%29%29=log%28%2810%5E%28y-3%29%29%29\"$
\n" ); document.write( " $\"log%28%28x-4%29%29=%28y-3%29log%2810%29\"$ Note the common log of 10=1
\n" ); document.write( " $\"log%28%28x-4%29%29=%28y-3%29%281%29\"$
\n" ); document.write( " $\"log%28%28x-4%29%29=y-3\"$
\n" ); document.write( " $\"log%28%28x-4%29%29%2B3=y-3%2B3\"$
\n" ); document.write( " $\"log%28%28x-4%29%29%2B3=y\"$ Replace y with f^-1(x)
\n" ); document.write( " $\"f%5E%28-1%29%28x%29=log%28%28x-4%29%29%2B3\"$
\n" ); document.write( "Happy Calculating!!!
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