Let [.] denote the greatest integer function.Consider f(x)={2−|x|,−1≤x≤1|x−2|−x,1<x≤3 and g(x)=⎧⎪⎨⎪⎩sinx−1,0≤x<π2[x]−cos(x−2),π2≤x≤π.Which of the following statements is/are CORRECT?

Let [.] denote the greatest integer function.Consider f(x)={2−|x|,�

1.	Let [.] denote the greatest integer function.Consider f(x)={2−\|x\|,−1≤x≤1\|x−2\|−x,1<x≤3 and g(x)=⎧⎪⎨⎪⎩sinx−1,0≤x<π2[x]−cos(x−2),π2≤x≤π.Which of the following statements is/are CORRECT?
Answer» Let $[.]$ denote the greatest integer function. Consider $f (x) = {\begin{matrix} 2 - \| x \|, & - 1 \leq x \leq 1 \| x - 2 \| - x, & 1 < x \leq 3 \end{matrix}$ and $g (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} sin x - 1, & 0 \leq x < \frac{π}{2} [x] - cos (x - 2), & \frac{π}{2} \leq x \leq π \end{matrix} .$ Which of the following statements is/are CORRECT?