Consider the functions f(x)=⎧⎪⎨⎪⎩|x|,x≤−1x1/5−1<x≤1(2−x)3,x>1 and g(x)=1(x+2)3−2x−cosx. Let p be the number of critical points on the graph of f(x) and q be the number of solutions of g(x)=0, then which of the following option(s) is/are correct?

Consider the functions f(x)=⎧⎪⎨⎪⎩|x|,x≤−1x1/5−1<x≤1(

1.	Consider the functions f(x)=⎧⎪⎨⎪⎩\|x\|,x≤−1x1/5−1<x≤1(2−x)3,x>1 and g(x)=1(x+2)3−2x−cosx. Let p be the number of critical points on the graph of f(x) and q be the number of solutions of g(x)=0, then which of the following option(s) is/are correct?
Answer» Consider the functions $f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} \| x \|, & x \leq - 1 x^{1 / 5} & - 1 < x \leq 1 (2 - x)^{3}, & x > 1 \end{matrix} and g (x) = \frac{1}{(x + 2)^{3}} - 2 x - cos x$ . Let $p$ be the number of critical points on the graph of $f (x) and q$ be the number of solutions of $g (x) = 0$ , then which of the following option(s) is/are correct?