Let f and g

Question

Let $f$ and $g$

Accepted Answer

$$
\begin{aligned}
& \text { Sol. } f(x)=\left\{\[\begin{gathered} x+1, x<0 \ \
1-x, 0 \leq x<1 \ x-1,1 \leq x \end{gathered}\end{aligned}$$\right. \\
\& g(x)=\left\{$$\begin{gathered} x+1, x<0 \ 1, x \geq 0 \end{gathered}$$\right. \\
\& g(f(x))=\left\{$$\begin{gathered} x+2, x<-1 \ 1, x \geq-1 \end{gathered}$$\right.

\]

$\therefore \mathrm{g}(\mathrm{f}(\mathrm{x}))$ is continuous everywhere

$\mathrm{g}(\mathrm{f}(\mathrm{x}))$ is not differentiable at $\mathrm{x}=-1$
Differentiable everywhere else.

Solutions · 1