AP EAMCET · Maths · Functions
If \(f: R \rightarrow R^2\) and \(g: R^{+} \rightarrow R\) are such that \(g\{f(x)\}=|\sin x| \quad\) and \(\quad f\{g(x)\}=(\sin \sqrt{x})^2\), then a possible choice for \(f\) and \(g\) is
- A \(f(x)=x^2, g(x)=\sin \sqrt{x}\)
- B \(f(x)=\sin x, g(x)=|x|\)
- C \(f(x)=\sin ^2 x, g(x)=\sqrt{x}\)
- D \(f(x)=x^2, g(x)=\sqrt{x}\)
Answer & Solution
Correct Answer
(C) \(f(x)=\sin ^2 x, g(x)=\sqrt{x}\)
Step-by-step Solution
Detailed explanation
Given, \(g\{f(x)\}=|\sin x|\) and \(\quad f\{g(x)\}=(\sin \sqrt{x})^2\) Let us consider \(f(x)=\sin ^2 x\) and \(g(x)=\sqrt{x}\) \(\therefore \quad f\{g(x)\}=f(\sqrt{x})=\left(\sin ^2 \sqrt{x}\right)=(\sin \sqrt{x})^2\) and…
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