SOLUTION: Given f(x)=-2x+3, determine f^-1(x)

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Question 164342: Given f(x)=-2x+3, determine f^-1(x)
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Given: f%28x%29+=+-2x%2B3 find the inverse f%5E%28-1%29%28x%29
f%28x%29+=+-2x%2B3 First, replace the f(x) with y to get:
y+=+-2x%2B3 Now exchange the x and y to get:
x+=+-2y%2B3 Now solve this for y by subtracting 3 from both sides.
x-3+=+-2y Divide both sides by -2.
%28x-3%29%2F-2+=+y Now replace the y with f%5E%28-1%29%28x%29 to get:
highlight%28f%5E%28-1%29%28x%29+=+-%28x-3%29%2F2%29
Check:
f%28f%5E%28-1%29%28x%29%29+=+-2%28-%28x-3%29%2F2%29%2B3
f%28f%5E%28-1%29%28x%29%29+=+%28x-3%29%2B3
f%28f%5E%28-1%29%28x%29%29+=+x