Question

Find a formula for the inverse of the function g(x) = x² - 4x, x ≥ 2?

Answer 1

To find the inverse of the function g(x) = x² - 4x, x ≥ 2, follow these steps: replace g(x) with y, swap x and y, make y the subject of the equation, use the quadratic formula to solve for y, simplify the equation. The inverse of the function is g⁻¹(x) = 2 ± √(4 + x).

Step-by-step explanation:

To find the inverse of a function, we need to swap the dependent and independent variables and solve for the new dependent variable. In this case, the function is g(x) = x² - 4x, x ≥ 2. To find the inverse, we can follow these steps:

1. Replace g(x) with y: y = x² - 4x
2. Swap x and y: x = y² - 4y
3. Make y the subject of the equation: y² - 4y - x = 0
4. Use the quadratic formula to solve for y: y = (4 ± √(16 + 4x)) / 2
5. Simplify the equation further: y = 2 ± √(4 + x)

So, the inverse of the function g(x) = x² - 4x, x ≥ 2 is g⁻¹(x) = 2 ± √(4 + x).