JEE Mains · Maths · STD 12 - 1. relation and function
Let \(\mathrm{f}: \mathrm{R}-\left\{\frac{-1}{2}\right\} \rightarrow \mathrm{R}\) and \(\mathrm{g}: \mathrm{R}-\left\{\frac{-5}{2}\right\} \rightarrow \mathrm{R}\) 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 :
- A \(\mathrm{R}-\left\{-\frac{5}{2}\right\}\)
- B \(R\)
- C \(R-\left\{-\frac{7}{4}\right\}\)
- D \(\mathrm{R}-\left\{-\frac{5}{2},-\frac{7}{4}\right\}\)
Answer & Solution
Correct Answer
(A) \(\mathrm{R}-\left\{-\frac{5}{2}\right\}\)
Step-by-step Solution
Detailed explanation
\( \mathrm{f}(\mathrm{x})=\frac{2 \mathrm{x}+3}{2 \mathrm{x}+1} ; \mathrm{x} \neq-\frac{1}{2} \) \( \mathrm{~g}(\mathrm{x})=\frac{|\mathrm{x}|+1}{2 \mathrm{x}+5}, \mathrm{x} \neq-\frac{5}{2}\) Domain of \(f(g(x))\) \(f(g(x))=\frac{2 g(x)+3}{2 g(x)+1}\) \(x \neq-\frac{5}{2}\) and…
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