SOLUTION: Find a formula for the inverse of the function. y = e^(4 − x)

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Question 1196625: Find a formula for the inverse of the function.
y = e^(4 − x)
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Find a formula for the inverse of the function.
y+=+e%5E%284+-x%29
to find inverse swap the variables
x=+e%5E%284+-y%29..........solve for y, take natural logarithm of bot sides
ln%28x%29=ln%28+e%5E%284+-y%29%29
ln%28x%29=%284+-y%29ln%28+e%29..............ln%28+e%29=1
ln%28x%29=4+-y
y=4+-ln%28x%29
f%5E-1%28x%29=4+-ln%28x%29-> inverse



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


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.

Another method which is often easier is to use the idea that an inverse function "un-does" what the function does.

The given function does the following to the input variable:

x
(1) subtract 4 --> x-4
(2) multiply by -1 --> 4-x
(3) raise e to that power --> e%5E%284-x%29

The inverse function must do the opposite operations, in the opposite order:

x
(1) take natural log --> ln%28x%29
(2) multiply by -1 --> -ln%28x%29
(3) add 4 --> -ln%28x%29%2B4

ANSWER: The inverse function is y=-ln%28x%29%2B4