Question 54199
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(x)= 11x-9}}}, find the inverse function {{{f^(-1)(x)}}}

1) Write the function as:{{{y = 11x-9}}} 
2) Swap the x and y: {{{x = 11y-9}}}
3) Solve for y: {{{y = (x+9)/11}}}
4) Write in inverse function form by replacing y with {{{f^(-1)(x)}}}: {{{f^(-1) = (x+9)/11}}}

Check: Recall that: {{{f(f^(-1)(x)) = x}}}
{{{f((x+9)/11) = 11((x+9)/11)-9}}} = x

Similarly for {{{g(x) = (x+11)/9}}}
1) Write as: {{{y = (x+11)/9}}}
2) Swap the variables: {{{x = (y+11)/9}}}
3) Solve for y: {{{y = 9x-11}}}
4) Write the inverse function form: {{{g^(-1)(x) = 9x-11}}}

Check: Recall that {{{g(g^(-1)(x)) = x}}}
{{{g(9x-11) = (9(x+11)/9)-11}}} = x