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 function of g(x)=-1/2x+3 is g^(-1)(x) = -2x + 6.

Step-by-step explanation:

To find the inverse function of g(x)=-1/2x+3, we need to switch the x and y variables and solve for y. Here's the step-by-step process:

1. Replace g(x) with y: y = -1/2x + 3
2. Swap x and y: x = -1/2y + 3
3. Solve for y: 2x = -y + 6 → y = -2x + 6

Therefore, the inverse function of g(x) is g^(-1)(x) = -2x + 6. Option D, g^(-1)(x) = -2(x-3), is not the correct answer.