Question

Consider two functions defined on R as f(x) = 2 + |x – 1| and g(x) = min (f(t)) where $x\le t\le x^2+x+1$. If $n_1$ denotes number of points of discontinuity of g(x) and $n_2$ denotes number of points where g(x) is non-differentiable then $(n_1+n_2)$ is equal to ___.

• A. 3

Answer 1

The correct option is A

3

$f\left(t\right)=\{\begin{array}{ccc}3-t& ;& t\le 1\\ t+1& ;& t>1\end{array}$

$Now,g\left(x\right)=\{\begin{array}{ccc}3-(x^2+x+1)& ;& xϵ[-1,0]\\ 2& ;& xϵ(-\infty ,-1)\cup (0,1)\\ x+1& ;& xϵ[1,\infty )\end{array}\therefore n_1=0,n_2=3\Rightarrow (n_1+n_2)=3$