Answer:
Option 2: [tex]f^{(-1)}(x) = -\frac{3}{4x}[/tex] is the correct answer.
Step-by-step explanation:
Given function is:
[tex]f(x) = -\frac{3}{4x}[/tex]
There are few steps to find inverse of a function. We will apply them one by one onto the function
Step 1: Replacing f(x) with y
[tex]y = -\frac{3}{4x}[/tex]
Step 2: Replacing y with x and x with y
[tex]x = -\frac{3}{4y}[/tex]
Step 3: Solving the equation in step 2 for y
[tex]x = -\frac{3}{4y}\\y = -\frac{3}{4x}[/tex]
Step 4: Replacing y with inverse of f
[tex]f^{(-1)}(x) = -\frac{3}{4x}[/tex]
Hence,
Option 2: [tex]f^{(-1)}(x) = -\frac{3}{4x}[/tex] is the correct answer.
