If f(x) = √(log10x^2). The set of values of x for which x is real is

Question

If f(x) = \(\sqrt{log_{10}x^2}\) . The set of values of x for which x is real is

(a) [– 1, 1] 

(b) [1, ∞) 

(c) (– ∞, –1] 

(d) [– ∞, – 1] ∪ [1, ∞)

Answer 1

Answer : (d) [– ∞, – 1] ∪ [1, ∞) 

f(x) = \(\sqrt{log_{10}\,x^2}\) is defined when 

log₁₀ x² ≥ 0 

⇒ x² ≥ 10⁰ = 1 

⇒ (x² – 1) ≥ 0 

⇒ (x + 1) (x – 1) ≥ 0 

⇒ x < – 1 and x > 1 

⇒ x ∈ (– ∞, – 1] ∪ [1, ∞).