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Domain of $\left(x^{2}+9 x-105\right)+\frac{1}{4-x^{2}}$ is
Option: 1
R

Option: 2
$R-\left \{ 2 \right \}$

Option: 3
$R-\left \{ -2,2 \right \}$

Option: 4
None of these

Answers (1)

best_answer

Let $\left(x^{2}+9 x-105\right)=f(x)$ and $\frac{1}{4-x^{2}}=g(x)$

$f(x)=$ $\left(x^{2}+9 x-105\right)$ is a polynomal so its domain is R.

$g(x): \frac{1}{4-x^{2}}$
Domain is $R-\left\{x: 4-x^{2}=0\right\}.$
$4-x^{2}=0 \Rightarrow x=2,-2$
So, we will have to remove 2 and $-2$ , as $4-x^{2}=0$ for these $x$ .
So domain $=R-\{-2,2\}$

Now, domain of $f(x)+g(x)$ is intersection of their domains

so, overall domain $=R-\{-2,2\}$

Posted by

Shailly goel

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