SOLUTION: Given the function g(x)=x+5/x+2, find the inverse function g^-1(x)

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Question 1015206: Given the function g(x)=x+5/x+2, find the inverse function g^-1(x)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

g%28x%29=%28x%2B5%29%2F%28x%2B2%29, to find the inverse function g%5E-1%28x%29, first replace g%28x%29 with y
y=%28x%2B5%29%2F%28x%2B2%29.....now swap x and y
x=%28y%2B5%29%2F%28y%2B2%29....solve for y
x%28y%2B2%29=%28y%2B5%29
xy%2B2x=y%2B5
xy-y=5-2x
y=%285-2x%29%2F%28x-1%29
so, g%5E-1%28x%29=%285-2x%29%2F%28x-1%29