Mark (√) against the correct answer in the following:Let \(f(x)=\fr

1.	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» 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, ∞)

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»

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, ∞)