Let $f$ and $g$ be two functions defined by $f(x)=\left\{\begin{array}{cc}x+1, & x < 0 \\ |x-1|, & x \geq 0\end{array}\right.$ and $\mathrm{g}(x)=\left\{\begin{array}{cc}x+1, & x < 0 \\ 1, & x \geq 0\end{array}\right.$ Then $(g \circ f)(x)$ is :

Question

Let $f$ and $g$ be two functions defined by

$f(x)=\left\{\begin{array}{cc}x+1, & x < 0 \\ |x-1|, & x \geq 0\end{array}\right.$ and $\mathrm{g}(x)=\left\{\begin{array}{cc}x+1, & x < 0 \\ 1, & x \geq 0\end{array}\right.$

Then $(g \circ f)(x)$ is :

continuous everywhere but not differentiable at $x=1$

differentiable everywhere

not continuous at $x=-1$

continuous everywhere but not differentiable exactly at one point

Solution

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