Let [f, g: R R] be defined as : [f(x)=|x-1| and g(x)= casese^x, & x 0 x+1, & x 0 .cases] T…

Question

Let $$f, g: \mathbf{R} \rightarrow \mathbf{R}$$ be defined as :

$$f(x)=|x-1| \text { and } g(x)= \begin{cases}\mathrm{e}^x, & x \geq 0 \ x+1, & x \leq 0 .\end{cases}$$

Then the function $f(g(x))$ is

Accepted Answer

$$\begin{aligned}
& f(x)= \begin{cases}x-1, & x \geq 1 \
1-x & x<0\end{cases} \
\& g(x)=\left\{\[\begin{array}{cc} e^x & ; \quad x \geq 0 \ x+1 & ; \quad x \leq 0 \end{array}\end{aligned}$$\right.
\]

$$\begin{aligned}
f(g(x)) & = \begin{cases}g(x)-1, & g(x) \geq 1 \
1-g(x) & g(x)<1\end{cases} \
\& =\left\{\[\begin{array}{cl} e^x-1 & x \geq 0 \ -x & x<0 \end{array}\end{aligned}$$\right.
\]

Solutions · 1