To find the inverse of a funciton, you must switch the “x” and the “y” variables. As you said B is not a choice, I will take that out.
In the work below, I will switch f(x) with y, it makes no difference in the equation. But you’ll have to switch back to f(x).
A.
y= 2x+1
Inverse:
x=2y+1
x-1=2y
(x-1)/2= y
y= (x-1)/2
A is not an inverse
C.
y=(x+1)/5
Inverse
x=(y+1)/5
5x=y+1
5x-1=y
y=5x-1
C. Is not an inverse
D.
y=3x+2
Inverse
x=3y+2
x-2=3y
(x/3)-(2/3)=y
y=(x/3)-(2/3)
f(x)=(x/3)-(2/3)
SO D is the answer
