Let f : R rightarrow R and g : R rightarrow R be defined begin array l f(x) = \ begin array l log e \,\,\,\,\,\,\,\,\,\,\,\,,x 0\e - x\,\,\,\,\,\,\,\,\,\,\,,x le 0end array .and\g(x) = \ begin array l x\,\,\,\,\,\,\,\,\,\,\,\,\,,x ge 0\\ e x \,\,\,\,\,\,\,\,\,\,\,,x < 0end array ..Then,\,gof\,:R to R\,\,is:end array

Mathematics · Functions

JEE Main 2024 — 1 February, Shift 1 — Question 11

Let $\mathrm{f}: \mathbf{R} \rightarrow \mathbf{R}$ and $\mathrm{g}: \mathbf{R} \rightarrow \mathbf{R}$ be defined

\begin{array}{l}f(x) = \left\{ \begin{array}{l}{\log _e}\,\,\,\,\,\,\,\,\,\,\,\,,x > 0\\e - x\,\,\,\,\,\,\,\,\,\,\,,x \le 0\end{array} \right.and\\g(x) = \left\{ \begin{array}{l}x\,\,\,\,\,\,\,\,\,\,\,\,\,,x \ge 0\\{e^x}\,\,\,\,\,\,\,\,\,\,\,,x < 0\end{array} \right..Then,\,gof\,:R \to R\,\,is:\end{array}

\begin{array}{l}g(f(x)) = \left\{ \begin{array}{l}\log ,\,f(x) \ge 0\\{e^{f(x)}},\,f(x) < 0\end{array} \right.\\g(x) = \left\{ \begin{array}{l}{e^{ - x}},\left( { - \infty ,0} \right]\\{e^{in\,x}}(0,1)\\In\,x,\left[ {1,\infty } \right)\end{array} \right.\end{array}

Graph of g(f(x))

G(f(x))Many one into

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