Verified answer

To find f^-1(x), let f(x) = y, interchange x and y, and then re-solve for y; the resulting value of y will be the inverse function.

So, letting f(x) = y gives:

y = 3x + 2.

Then, interchanging x and y:

x = 3y + 2.

Solving this resulting equation for y yields:

y = (x - 2)/3.

Therefore, f^-1(x) = (x - 2)/3.

Let g(x) be inverse function

Let y = f (x) = 3x + 2 and g (y) = x

3x = y - 2

x = (y - 2) / 3

g (y) = (y - 2) / 3

g (x) = (x - 2) / 3

f(x)=3x+2

y = 3x+2

3x = y-2

x = (y-2)/3

for the inverse of x, replace y with x

f^-1(x) = (x-2)/3

y=3x+2

Interchange x and y

x=3y+2

solve for y

x-2=3y

y=(x-2)/3

f^(-1)(x) =(x-2)/3