Functions Question 9
Question 9 - 29 January - Shift 1
The domain of $f(x)=\frac{\log _{(x+1)}(x-2)}{e^{2 \log _e x}-(2 x+3)}, x \in R$ is
(1) $\mathbb{R}-{1-3}$
(2) $(2, \infty)-{3}$
(3) $(-1, \infty)-{3}$
(4) $\mathbb{R}-{3}$
Show Answer
Answer: (2)
Solution:
Formula: Domain of function, Properties of logarithmic function, Properties of exponential function
$x-2>0 \Rightarrow x>2$
$x+1>0 \Rightarrow x>-1$
$x+1 \neq 1 \Rightarrow x \neq 0$ and $x>0$
Denominator
$x^{2}-2 x-3 \neq 0$
$(x-3)(x+1) \neq 0$
$x \neq-1,3$
So Ans $(2, \infty)-{3}$
