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

Question

The domain of the function f(x) =( log (x+5)/x2 +4x +3) is (A)  (-∞, -1)  (B)  [-3, -1]  (C)  R-[-3, -1]  (D)  (-5, ∞) - -3, -1

Tardigrade Admin · Accepted Answer

We have, f (x) =(log(x+5)/x2+4x+3) =(log(x+5)/(x+3)(x+1)) f (x) will be defined, if x+3≠0, x+1≠0 and x+5 > 0 i.e, x ≠-3, x ≠-1 and x > -5 ∴ Domain of function is (-5, ∞)- -3,-1

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

$(- \infty, - 1)$

$[- 3, - 1]$

$R - [- 3, - 1]$

$(- 5, \infty) - {- 3, - 1}$

We have,
$f (x) = \frac{l o g ( x + 5 )}{x ^{2} + 4 x + 3}$
$= \frac{l o g ( x + 5 )}{( x + 3 ) ( x + 1 )}$
$f (x)$ will be defined, if $x + 3 \neq = 0$ ,
$x + 1 \neq = 0$
and $x + 5 > 0$ i.e, $x \neq = - 3$ ,
$x \neq = - 1$ and $x > - 5$
$∴$ Domain of function is $(- 5, \infty) - {- 3, - 1}$

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

(−∞,−1)

[−3,−1]

R−[−3,−1]

(−5,∞)−{−3,−1}