Question 392564
f(x)=9x-5_f^(-1)(5)

To find the inverse of the function, interchange the variables and solve for f^(-1)(x).
x=9f^(-1)(x)-5

Since f^(-1)(x) is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
9f^(-1)(x)-5=x

Since -5 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 5 to both sides.
9f^(-1)(x)=5+x

Move all terms not containing f^(-1)(x) to the right-hand side of the equation.
9f^(-1)(x)=x+5

Divide each term in the equation by 9.
(9f^(-1)(x))/(9)=(x)/(9)+(5)/(9)

Simplify the left-hand side of the equation by canceling the common factors.
f^(-1)(x)=(x)/(9)+(5)/(9)

Combine the numerators of all expressions that have common denominators.
f^(-1)(x)=(x+5)/(9)

Evaluate the inverse f^(-1) at x=5.
f^(-1)(5)=((5)+5)/(9)

Simplify the function.
f^(-1)(5)=(10)/(9)