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  4. The domain of the function f(x) =( log (x+5)/x2 +4x +3) is

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Q. The domain of the function $ f\left(x\right) =\frac{ log \left(x+5\right)}{x^{2} +4x +3} $ is

J & K CETJ & K CET 2017Relations and Functions

Solution:

We have,
$f (x) =\frac{log(x+5)}{x^{2}+4x+3}$
$=\frac{log\left(x+5\right)}{\left(x+3\right)\left(x+1\right)}$
$f (x)$ will be defined, if $x+3\ne0$,
$x+1\ne0$
and $x+5 >\,0$ i.e, $x \ne-3$,
$x \ne-1$ and $x >\,-5 $
$\therefore $ Domain of function is $\left(-5, \infty\right)-\left\{-3,-1\right\}$