Question

Find the inverse of the function G(x) = 3(x - 1), denoted as G^-1(x).

Answer 1

To find the inverse of the function G(x) = 3(x - 1), denoted as G^-1(x), follow these steps:

Replace G(x) with y:

y = 3(x - 1)

Swap the roles of x and y:

x = 3(y - 1)

Solve for y:

x = 3(y - 1)

Divide both sides by 3:

(1/3)x = y - 1

Add 1 to both sides to isolate y:

(1/3)x + 1 = y

Now, replace y with G^-1(x):

G^-1(x) = (1/3)x + 1

So, the inverse of the function G(x) = 3(x - 1) is G^-1(x) = (1/3)x + 1.

Explanation: