Question

Find the inverse of the function y = x² - 4x.

a) y = (x - 2)²
b) y = (x + 2)²
c) y = (x - 2)(x + 2)
d) y = (x + 2)(x - 4)

Answer 1

To find the inverse of the function y = x² - 4x, replace y with x and x with y, rearrange the equation to solve for y, use the quadratic formula to find the solutions for y, and simplify the equation for y. The inverse of the function y = x² - 4x is y = (4 ± √(16 + 4x)) / 2.

Step-by-step explanation:

To find the inverse of the function y = x² - 4x, we need to interchange the roles of x and y in the equation and solve for y.

Step 1: Replace y with x and x with y: x = y² - 4y

Step 2: Rearrange the equation to solve for y: y² - 4y - x = 0

Step 3: Use the quadratic formula to find the solutions for y: y = (-(-4) ± √((-4)² - 4(1)(-x))) / (2(1))

Step 4: Simplify the equation for y: y = (4 ± √(16 + 4x)) / 2

So, the inverse of the function y = x² - 4x is y = (4 ± √(16 + 4x)) / 2.