The function $y = \frac{2x - 1}{x - 2}$ $(x \neq 2)$:

The function $f(x) = |px - q| + r|x|$,$x \in (-\infty, \infty)$,where $p > 0, q > 0, r > 0$ assumes its minimum value only at one point,if

Let $f(x) = -1 + |x - 2|$ and $g(x) = 1 - |x|$. Then the set of all points where $fog$ is discontinuous is

If $f(x)=\frac{2^{x}+2^{-x}}{2}$,then $f(x+y) \cdot f(x-y)$ is

Let $f:[0,2] \rightarrow R$ be the function defined by $f(x)=(3-\sin(2\pi x)) \sin(\pi x-\frac{\pi}{4})-\sin(3\pi x+\frac{\pi}{4})$. If $\alpha, \beta \in[0,2]$ are such that $\{x \in[0,2]: f(x) \geq 0\}=[\alpha, \beta]$,then the value of $\beta-\alpha$ is:

$ A $ is a set having $ 6 $ distinct elements. The number of distinct functions from $ A $ to $ A $ which are not bijections is