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

1.	Mark (√) against the correct answer in the following:Let \(f(x)=\frac{x^2}{(1+x^2)}\) Then, range (f) = ?A. [1, ∞) B. [0, 1) C. [ - 1, 1] D. (0, 1]
Answer» Correct Answer is (B) = [0, 1) \(f(x)=\frac{x^2}{1+x^2}\) ⇒ \(y=\frac{x^2}{1+x^2}\) ⇒ y + yx² = x² ⇒ y = x² (1 - y) ⇒ x = \(\sqrt{\frac{y}{1-y}}\) \(\frac{y}{1-y}\geq 0\) ⇒ y ≥ 0 And 1 - y > 0 ⇒ y < 1 Taking intersection we get range (f) = [0, 1)

Mark (√) against the correct answer in the following:Let \(f(x)=\frac{x^2}{(1+x^2)}\) Then, range (f) = ?A. [1, ∞) B. [0, 1) C. [ - 1, 1] D. (0, 1]

Answer»

Correct Answer is (B) = [0, 1)

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

⇒ \(y=\frac{x^2}{1+x^2}\)

⇒ y + yx² = x²

⇒ y = x² (1 - y)

⇒ x = \(\sqrt{\frac{y}{1-y}}\)

\(\frac{y}{1-y}\geq 0\)

⇒ y ≥ 0

And

1 - y > 0

⇒ y < 1

Taking intersection we get

range (f) = [0, 1)