document.write( "Question 1196625: Find a formula for the inverse of the function.
\n" ); document.write( "y = e^(4 − x) \n" ); document.write( "

Algebra.Com's Answer #829549 by greenestamps(13203) $\"\"$ $\"About$

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\n" ); document.write( "The response from the other tutor shows the method which is usually taught for finding the inverse of a function: switch the x and y and solve for the new y.

\n" ); document.write( "Another method which is often easier is to use the idea that an inverse function \"un-does\" what the function does.

\n" ); document.write( "The given function does the following to the input variable:

\n" ); document.write( " $\"x\"$
\n" ); document.write( "(1) subtract 4 --> $\"x-4\"$
\n" ); document.write( "(2) multiply by -1 --> $\"4-x\"$
\n" ); document.write( "(3) raise e to that power --> $\"e%5E%284-x%29\"$

\n" ); document.write( "The inverse function must do the opposite operations, in the opposite order:

\n" ); document.write( " $\"x\"$
\n" ); document.write( "(1) take natural log --> $\"ln%28x%29\"$
\n" ); document.write( "(2) multiply by -1 --> $\"-ln%28x%29\"$
\n" ); document.write( "(3) add 4 --> $\"-ln%28x%29%2B4\"$

\n" ); document.write( "ANSWER: The inverse function is $\"y=-ln%28x%29%2B4\"$

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