[tex]y= \frac{-3}{x+4} [/tex]
Step 1: Isolating x on one side of the equation.
[tex]y(x+4)=-3 \\ \\
x+4= \frac{-3}{y} \\ \\
x= \frac{-3}{y}-4 [/tex]
Step 2: Replace x by f'(y)
[tex]f'(y)= \frac{-3}{y}-4 [/tex]
Step 3: Replace each occurrence of y by x
[tex]f'(x)= \frac{-3}{x}-4 \\ \\
f'(x)= \frac{-3-4x}{x} [/tex]
Thus, option D gives the correct inverse of the given function
