SOLUTION: Find the inverse of the following function g(x) = e^x -2e^x / 2

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Question 1154019: Find the inverse of the following function
g(x) = e^x -2e^x / 2
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

g%28x%29+=+%28e%5Ex+-2e%5Ex%29+%2F+2 inverse
g%28x%29+=+y
y=+%28e%5Ex+-2e%5Ex%29+%2F+2 .........swap variables
x=+%28e%5Ey+-2e%5Ey%29+%2F+2
2x=+e%5Ey+-2e%5Ey
2x=+-e%5Ey.......switch sides
e%5Ey=+-2x......take log of both sides
ln%28e%5Ey%29=+ln%28-2x%29
y%2Aln%28e%29=+ln%28-2x%29...........ln%28e%29=1
y=+ln%28-2x%29
=>+g%5E-1%28x%29+=ln%28-2x%29