Select the statement that is correct about the inverse of g(x)=x/3 -2

Question

1)the inverse is g^-1 (x)=3x+2
2)the inverse is g^-1 (x)=3x+6
3)the inverse is g^=1 (x)=-
4)the inverse does not exist because the function is not one-to-one

Answer 1

To find the inverse of the function \( g(x) = \frac{x}{3} - 2 \), we first need to solve for \( x \) in terms of \( y \):

1. Start by setting \( y = g(x) \): \[ y = \frac{x}{3} - 2 \]

2. Rearrange the equation to solve for \( x \): \[ y + 2 = \frac{x}{3} \] \[ x = 3(y + 2) \] \[ x = 3y + 6 \]

3. Now, express this as the inverse function: \[ g^{-1}(x) = 3x + 6 \]

So, the correct statement is: 2) the inverse is \( g^{-1}(x) = 3x + 6 \).