Let f(x) = 1/(1 - x^2). Then, range (f) = ?

Question

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

Let \(f(x)=\frac{1}{(1-x^2)}\). Then, range (f) = ?

A. ( - ∞, 1] 

B. [1, ∞) 

C. [ - 1, 1] 

D. none of these

Answer 1

Correct Answer is (B) [1, ∞)

\(f(x)=\frac{1}{1-x^2}\)

\(\Rightarrow y= \frac{1}{1-x^2}\)

⇒ y - yx² = 1

⇒ y - 1 = yx²

⇒ \(x=\sqrt{\frac{y-1}{y}}\)

⇒ \(\frac{y-1}{y}\geq 0\)

⇒ y ≥ 1

∴ range (f) = [1, ∞)