Let f:R R and g:R R be defined as f(x)= array|c|c| _ex, & x0 e^-x, & x 0 array and g(x)= …

Question

Let $f:R	o R$ and $g:R	o R$ be defined as

$f(x)= \begin{array}{|c|c|} {\log }_{e}x, & x>0 \ {e}^{-x}, & x\le 0 \end{array}$ and

$g(x)= \begin{array}{|c|c|} x, & x\geqslant 0 \ {e}^{x}, & x<0 \end{array}$. Then, gof : $R	o R$ is :

Accepted Answer

Given, $f(x)= \begin{gathered} {\log }_{e}x, x>0 \ {e}^{-x}, x\le 0 \end{gathered}$ and

$g(x)= $$x, \& x\geqslant 0  \  {e}^{x}, \& x$$

From the graph of $g(f(x))$, we can say

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Solutions · 1