Let f and g be two functions defined by f (x) = \ array ll x + 1, x...

Given,

$f$\left(x\right) = \left\{$$\begin{array}{ll}x + 1, x < 0 \\ \left|x - 1\right|, x \ge 0\end{array}$$\right)and g\left(x\right) = \left\{$\begin{array}{ll}x + 1, x < 0 \\ 1, x \ge 0\end{array}$\right)</p><p>⇒ f\left(x\right) = \left\{$\begin{cases}x + 1, & x 1\end{cases}$ \text{ and } g\left(x\right) = \left\{$\begin{cases}1 + x, & x < 0 \\ 1, & x \ge 0\end{cases}$\right\right)

Now, for $gof\left(x\right)$

gof\left(x\right) = \left\{\begin{cases}1 + f\left(x\right), & f\left(x\right) < 0, x < 0 \\ 1, & f\left(x\right) \ge 0, x \ge 0\end{cases}\right)</p><p>⇒ gof\left(x\right) = \left\{$\begin{cases}x + 2, & x < - 1 \\ 1, & x \ge - 1\end{cases}$\right)

Now plotting the diagram we get,

Now from above diagram we can say that function is continuous but not differentiable at $x = - 1$ due to sharp corner.