Let f, g: $R \rightarrow R$ be functions defined by $f ( x )=\left\{\begin{array}{ll}{[ x ]} & , \quad x < 0 \\ |1- x | & , \quad x \geq 0\end{array}\right.$ and $g(x)=\left\{\begin{array}{ll}e^{x}-x & , x < 0 \\ (x-1)^{2}-1 & , \quad x \geq 0\end{array}\right.$ where $[ x ]$ denote the greatest integer less than or equal to $x$. Then, the function fog is discontinuous at exactly
→Assume $X,\, Y,\, Z, W$ and $P$ are the matrices of order $2 \times n, \,3 \times k,\, 2 \times p, \,n \times 3$ and $p \times k$ respectively. The restriction on $n,\, k$ and $p$ so that $P Y+W Y$ will be defined are :
→If the function $f$ defined on $\left( {\frac{\pi }{6},\frac{\pi }{3}} \right)$ by $f\,(x)\, = \,\left\{ {\begin{array}{*{20}{c}}
{\frac{{\sqrt 2 \,\cos \,x - \,1}}{{\cot \,x\, - \,1}}\,,\,x\, \ne \,\frac{\pi }{4}}\\
{k,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\, = \frac{\pi }{4}}
\end{array}} \right.$ is continuous, then $k$ is equal to
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