Let f(x) √x-1/x+4. then, dom(f) - ?

Question

Mark (√) against the correct answer in the following: 

Let \(f(x)\sqrt{\frac{x-1}{x+4}}\) Then, dom (f) - ? 

A. [1, 4) 

B. [1, 4] 

C. ( - ∞, 4] 

D. ( - ∞, 1] ∪ (4, ∞)

Answer 1

Correct Answer is (D) ( - ∞, 1] ∪ (4, ∞)

\(f(x)\sqrt{\frac{x-1}{x+4}}\)

\(\sqrt{\frac{x-1}{x-4}}\geq0\)

\(\Rightarrow x-1\geq0\)

\(\Rightarrow x\geq1\)

And x≠4

x > 4 and x ≤ 1

⇒ dom (f) = ( - ∞, 1] ∪ (4, ∞)