Question

Determine the inverse of the function g(x) = -2/3x - 5.

a) g⁻¹(x) = -3/2x + 5
b) g⁻¹(x) = -3/2x - 5
c) g⁻¹(x) = -2/3x + 5
d) g⁻¹(x) = -2/3x - 5

Answer 1

To find the inverse of the function g(x) = -2/3x - 5, switch x and y, solve for y, and the inverse is g⁻¹(x) = -3/2x + 5.

Step-by-step explanation:

To find the inverse of the function g(x) = -2/3x - 5, we need to switch the roles of x and y and solve for y. Let's start:

1. Replace g(x) with y: y = -2/3x - 5
2. Switch x and y: x = -2/3y - 5
3. Solve for y: add 5 to both sides and multiply by -3/2: y = -3/2x + 5

Therefore, the inverse of g(x) is g-1(x) = -3/2x + 5. So the correct answer is a) g-1(x) = -3/2x + 5.