Let \( \quad f(x)=\left\{\begin{array}{cc}x+a, & \text { if } x0 \\ |x-1|, & \text { if } x \geq...

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Let \( \quad f(x)=\left\{\begin{array}{cc}x+a, & \text { if } x0 \\ |x-1|, & \text { if } x \geq 0\end{array}\right. \)
and
P \( g(x)=\left\{\begin{array}{cc}x+1, & \text { if } x0 \\ (x-1)^{2}+b, & \text { if } x \geq 0\end{array}\right. \)

W
where, \( a \) and \( b \) are non-negative real numbers. Determine the compositie function gof. If (gof) \( (x) \) is continuous for all real \( x \) determine the values of \( a \) and \( b \). Further, for these values of \( a \) and \( b \), is gof differentiable at \( x=0 \) ? Justify your answer.
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