Question

Given the function:

g(x) = -1/2x + 3

What is the inverse function of g(x)?

a) g^(-1)(x) = -2x - 3
b) g^(-1)(x) = -3(x - 3)
c) g^(-1)(x) = -3x - 2
d) g^(-1)(x) = -2(x - 3)

Answer 1

The inverse of the function g(x) = -1/2x + 3 is g^(-1)(x) = -2(x - 3).

Step-by-step explanation:

The inverse of the function g(x) = -1/2x + 3 is:

g-1(x) = -2(x - 3)

To find the inverse function, we need to swap the x and y variables and solve for y. Let's start:

1. Replace g(x) with y: y = -1/2x + 3
2. Swap x and y: x = -1/2y + 3
3. Isolate y: 2x = -y + 6
4. Multiply both sides by -1: -2x = y - 6
5. Rearrange to get y by itself: y = -2x + 6

So, the inverse function of g(x) is g-1(x) = -2(x - 3).