COMEDK · Maths · 24. Functions
If \(f(x)=e^{x}\) and \(g(x)=\log e^{x}\), then which of the following is true?
- A \(f\{g(x)\} \neq g\{f(x)\}\)
- B \(f\{g(x)\}=g\{f(x)\}\)
- C \(f\{g(x)\}+g\{f(x)\}=0\)
- D \(f\{g(x)\}-g\{f(x)\}=1\)
Answer & Solution
Correct Answer
(B) \(f\{g(x)\}=g\{f(x)\}\)
Step-by-step Solution
Detailed explanation
We have, \(f(x)=e^{x}\) and \(g(x)=\log e^{x}\) Now, \(f(g(x))=f\left(\log e^{x}\right)=e^{\log e^{x}}=e^{x}\) and \(g(f(x))=g\left(e^{x}\right)=\log e^{e^{x}}=e^{x} \log e=e^{x}\) Hence, \(f(g(x))=g(f(x))\).
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