Functions Question 4
Question 4 - 2024 (27 Jan Shift 2)
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 fog is :
(1) $R-{-\frac{5}{2} }$
(2) R
(3) $R-{-\frac{7}{4} }$
(4) $R-{-\frac{5}{2},-\frac{7}{4} }$
Show Answer
Answer (1)
Solution
$f(x)=\frac{2 x+3}{2 x+1} ; x \neq-\frac{1}{2}$
$g(x)=\frac{|x|+1}{2 x+5}, x \neq-\frac{5}{2}$
Domain of $f(g(x))$
$f(g(x))=\frac{2 g(x)+3}{2 g(x)+1}$
$\mathbf{x} \neq-\frac{5}{2}$ and $\frac{|x|+1}{2 x+5} \neq-\frac{1}{2}$
$x \in R-{-\frac{5}{2} }$ and $x \in R$
$\therefore$ Domain will be $R-{-\frac{5}{2} }$
