Question

Domian of function √x2-5x+4

Answer 1

f(x) = $\sf \sqrt{x^{2} - 5x + 4 }$

Domain restriction of the square root function, everything in the square root must be greater than or equal to 0.

So,

☛ x² - 5x + 4 ≥ 0

☛ x² - x - 4x + 4 ≥ 0

☛ x(x - 1) - 4(x - 1) ≥ 0

☛ (x - 1)(x - 4) ≥ 0

By wavy curve method,

x ∈ (-∞ , 1] ∪ [4, ∞)