Range of the expression fx - x2-1x2-1- x- is

Let y = x^2 1x^2+1 ⇒ (y 1)x^2 + (y+1)=0 ⇒ y≠1 because coefficient of x^2 can not be 0. x ∈ℝ⇒Δ≥ 0 ⇒ 4 (y 1)(y+1) ≥ 0 ⇒ nbsp; (y^2 1)≤ 0 ⇒ nbsp; y ∈ [ 1,1] ∴ ...

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Standard XII

Mathematics

Range of Quadratic Expression

Range of the ...

Question

Range of the expression $f (x) = \frac{x^{2} - 1}{x^{2} + 1}, x \in R$ is

[- 1, 1]

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[- 1, 1)

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(- 1, 1)

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(- 1, 1]

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Solution

The correct option is B $[- 1, 1)$
Let
$y = \frac{x^{2} - 1}{x^{2} + 1} \Rightarrow (y - 1) x^{2} + (y + 1) = 0$
$\Rightarrow y \neq 1$ because coefficient of $x^{2}$ can not be $0.$
$x \in R \Rightarrow Δ \geq 0 \Rightarrow - 4 (y - 1) (y + 1) \geq 0 \Rightarrow (y^{2} - 1) \leq 0$
$\Rightarrow y \in [- 1, 1]$
$∴ Range of y = [- 1, 1)$

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Range of Quadratic Expression

Standard XII Mathematics

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Range of the expression f(x)=x2−1x2+1, x∈R is

The correct option is B [−1,1)Let y=x2−1x2+1⇒(y−1)x2+(y+1)=0 ⇒y≠1 because coefficient of x2 can not be 0. x∈R⇒Δ≥0⇒−4(y−1)(y+1)≥0⇒(y2−1)≤0 ⇒y∈[−1,1] ∴Range of y=[−1,1)

Range of the expression $f (x) = \frac{x^{2} - 1}{x^{2} + 1}, x \in R$ is