JEE Mains · Maths · STD 12 - 1. relation and function
Let \(\mathrm{f}: R \rightarrow R\) and \(\mathrm{g}: R \rightarrow R\) be defined as \(f(x)=\left\{\begin{array}{lll}\log _e x & , & x>0 \\ e^{-x} & , & x \leq 0\end{array}\right.\) and \(g(x)=\left\{\begin{array}{lll} x & , & x \geq 0 \\ e^{x} & , & x < 0\end{array}\right.\) Then \(gof:R \to R\) is ...........
- A one-one but not onto
- B neither one-one nor onto
- C onto but not one-one
- D both one-one and onto
Answer & Solution
Correct Answer
(B) neither one-one nor onto
Step-by-step Solution
Detailed explanation
\(\mathrm{g}(\mathrm{f}(\mathrm{x}))=\left\{\begin{array}{l}f(x), f(x) \geq 0 \\ e^{f(x)}, f(x)<0\end{array}\right.\) \(\mathrm{g}(\mathrm{f}(\mathrm{x}))=\left\{\begin{array}{l}e^{-x},(-\infty, 0] \\ e^{\ln x},(0,1) \\ \ln x,[1, \infty)\end{array}\right.\) Graph of \(g(f(x))\)…
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