Question

If $f\left(x\right)=|x|,g\left(x\right)=\left\{\begin{array}{ccc}4-(x+4{)}^2& ;& xϵ(-5,-1)\\ x^3-x^2& ;& xϵ[-1,1)\end{array}\right\}$

Let $\alpha$ be no. of points of local extremum and $\beta$ be the number of points of non-differentiability of f(g(x)) then $\alpha +\beta$ is equal to

• A. 3
• B. 5
• C. 6
• D. 8

Answer 1

The correct option is C 6

$f\left(g\right(x\left)\right)=|g\left(x\right)|=\left\{\begin{array}{ccc}|4-(x+4{)}^2|& ;& xϵ(-5,-1)\\ |x^3-x^2|& ;& xϵ[-1,1]\end{array}\right\}$

graph of f(g(x)) is

So $\alpha =4,\beta =2$

$\alpha +\beta =6$