Jee Main 2024 27 01 2024 Shift 2 - Question7
Question 7
Let $f: R{-\frac{1}{2} } \rightarrow R$ and $g: R-{-\frac{5}{2} } \rightarrow R$ be defined as $f(x)=\frac{2 x+3}{2 x+1}$ and $g(x)=\frac{|x|+1}{2 x+5}$ then the domain of the function $f(g(x))$ is
$R$
(2) $R-{-\frac{5}{2} }$
(3) $R-{-\frac{1}{2},-\frac{5}{2} }$
(4) $R-{-\frac{1}{2} }$
Show Answer
Answer: (2)
Solution:
$f(g(x))$
$$ \Rightarrow \quad g(x) \neq-\frac{1}{2} $$
$$ \frac{|x|+1}{2 x+5} \neq \frac{-1}{2} $$
(I) $x \geq 0$
$\frac{x+1}{2 x+5}=\frac{-1}{2}$
$2 x+2=-2 x-5$
$4 x=-7$
$x=\frac{-7}{4}($ Rejected $)$ (II) $x<0$
$$ \begin{aligned} & \frac{-x+1}{2 x+5}=\frac{-1}{2} \\ & -2 x+2=-2 x-5 \end{aligned} $$
$2=-5$ (not possible)
$\Rightarrow$ Domain of $f(g(x))=$ domain of $g(x)$ where $g(x)$ is in the domain of $f$
$$ D _{fog}=R-{\frac{5}{2} } $$
BETA
