Question

If x - 4 = z, z - 2 = y and xz > yz then find the range of x.

1. x < -4
2. x > 4
3. x > 0
4. x < 6

Answer 1

Correct Answer - Option 2 : x > 4

Calculation:

xz > yz

⇒ xz = x × (x - 4) = x² - 4x

⇒ yz = (z - 2) × z = z² - 2z = (x - 4)² - 2(x - 4) = x² - 8x + 16 - 2x + 8 = x² - 10x + 24

Then,

⇒ x² - 4x > x² - 10x + 24

⇒ 6x > 24

⇒ x > 4

∴ Range of x is x > 4.

Range is set of maximum and minimum value of function.