SOLUTION: I do not know how to solve this problem f(x)= 11x-9 g(x)= x+11 over 9 verify the inverse functions

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Question 54199: I do not know how to solve this problem

f(x)= 11x-9 g(x)= x+11 over 9


verify the inverse functions
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
To find the inverse of a function, you exchange the dependent and the independent variables, then solve for the dependent variable. Sounds complicated doesn't it? But here's how it's done:
Given the function f%28x%29=+11x-9, find the inverse function f%5E%28-1%29%28x%29
1) Write the function as:y+=+11x-9
2) Swap the x and y: x+=+11y-9
3) Solve for y: y+=+%28x%2B9%29%2F11
4) Write in inverse function form by replacing y with f%5E%28-1%29%28x%29: f%5E%28-1%29+=+%28x%2B9%29%2F11
Check: Recall that: f%28f%5E%28-1%29%28x%29%29+=+x
f%28%28x%2B9%29%2F11%29+=+11%28%28x%2B9%29%2F11%29-9 = x
Similarly for g%28x%29+=+%28x%2B11%29%2F9
1) Write as: y+=+%28x%2B11%29%2F9
2) Swap the variables: x+=+%28y%2B11%29%2F9
3) Solve for y: y+=+9x-11
4) Write the inverse function form: g%5E%28-1%29%28x%29+=+9x-11
Check: Recall that g%28g%5E%28-1%29%28x%29%29+=+x
g%289x-11%29+=+%289%28x%2B11%29%2F9%29-11 = x