SOLUTION: If f(x)=4-3x, find f^(-1)(-41)

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Question 176268: If f(x)=4-3x, find f^(-1)(-41)
Answer by EMStelley(208) About Me  (Show Source):
You can put this solution on YOUR website!
First, you need to find the inverse function for f. This is done by first replacing f(x) with y,
y=4-3x
Next, you swap the two variables.
x=4-3y
And lastly, you solve for y so that it is in y= format again.
x-4=-3y
y=%28-1%2F3%29x%2B4%2F3
This is the inverse function:
f%5E-1x=%28-1%2F3%29x%2B4%2F3
So if we want to evaluate the inverse function at -41, we just plug in -41 for x now and obtain that
f^(-1)(-41)=(-1/3)(-41)+4/3=(41/3)+4/3=45/3=15