Answer:
[tex]f^{-1}(x) = \displaystyle\frac{4x}{3} +12[/tex]
Step-by-step explanation:
We are given the following function in the question:
[tex]f(x) = \displaystyle\frac{3}{4}x-9[/tex]
We have to find the inverse of the given function.
To find the inverse we solve for x and then interchange the variable.
[tex]y = \displaystyle\frac{3}{4}x - 9\\\frac{3}{4}x = y + 9\\x = \frac{4}{3}(y+9)\\\\x = \frac{4y}{3}+12[/tex]
Thus, the inverse of the function is
[tex]f^{-1}(x) = \displaystyle\frac{4x}{3} +12[/tex]
