Question

Let $f(x)=\{\begin{array}{ll}2\ln (-x-1),& -e-1\le x\le -2\\ \frac{1}{2}\left(4-x^2\right),& -2<x<0\\ 0,& x=0\\ \frac{1}{2}\left(x^2-4\right),& 0<x<2\\ \frac{2}{2}\ln (x-1),& 2\le x\le e+1\end{array}$

and graph of $f(x)$ is as shown

If the equation $g(x)=k$ has exactly two distinct solutions in $[-e-1,e+1]$ then the sum of all possible integral values of $k$ is

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (D)

Correct answer is (d) 3