The function $f(x) = 2x - |x - x^2|$ is

If the function $f$ is continuous at $x = 1$, where $f(x) = \frac{1 + \cos(\pi x)}{\pi(1-x)^2}$ for $x \neq 1$, then the value of $f(1)$ is....

If $f(x) = \begin{cases} ax + 7, & \text{if } x < 1 \\ 3x - 1, & \text{if } x = 1 \\ \frac{x + 3}{b}, & \text{if } x > 1 \end{cases}$ is continuous at $x = 1$, then

If a real valued function $f(x) = \begin{cases} \log(1+[x]), & x \geq 0 \\ \sin^{-1}[x], & -1 \leq x < 0 \\ k([x]+|x|), & x < -1 \end{cases}$ is continuous at $x = -1$,then $k =$

Which of the following statements is true for the graph of the function $f(x) = \log x$?

Discuss the continuity of the following functions:
a) $f(x) = \sin x + \cos x$
b) $f(x) = \sin x - \cos x$
c) $f(x) = \sin x \times \cos x$