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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\; g(x)=\left\{\begin{array}{cc}x+1, & x<0 \\ 1, & x \geq 0\end{array}\right. Then (gof) \left ( x \right ) is

Option: 1

continuous everywhere but not differentiable at x=1


Option: 2

continuous everywhere but not differentiable exactly at one point


Option: 3

 differentiable everywhere


Option: 4

not continuous at x=-1


Answers (1)

best_answer

f(x)=\left\{\begin{array}{l}x+1, x<0 \\ 1-x, 0 \leq x<1 \\ x-1,1 \leq x\end{array}\right.
g(x)=\left\{\begin{array}{l}x+1, x<0 \\ 1, x \geq 0\end{array}\right.

g(f(x))=\left\{\begin{array}{l}x+2, x<-1 \\ 1, x \geq-1\end{array}\right.

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

g(\mathrm{f}(\mathrm{x})) is not differentiable at \mathrm{x}=-1

Differentiable everywhere else

Posted by

Nehul

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