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

Question:

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

Let $f(x)=\frac{1}{\left(1-x^{2}\right)} \cdot$ Then, range $(f)=?$

A. $(-\infty, 1]$

B. $[1, \infty)$

C. $[-1,1]$

D. none of these

 

Solution:

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

$\Rightarrow \mathrm{y}=\frac{1}{1-\mathrm{x}^{2}}$

$\Rightarrow \mathrm{y}-\mathrm{yx}^{2}=1$

$\Rightarrow \mathrm{y}-1=\mathrm{yx}^{2}$

$\Rightarrow x=\sqrt{\frac{y-1}{y}}$

$\Rightarrow \frac{y-1}{y} \geq 0$

$\Rightarrow \mathrm{y} \geq 1$

$\therefore$ range $(f)=[1, \infty)$

 

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