# Many functions

Calculus Level 5

$\large f(x) = \begin{cases}{\{ x \} \cdot \sqrt { 4{ x }^{ 2 }-12x+9 } ,} && {1\le\>x\le\>2} \\ {\cos\left( \frac { \pi }{ 2 } (|x|-\{ x\} ) \right) ,} && {\>-1\le\>x<1}\end{cases}$

Consider the piecewise function $$f(x)$$ above with $$\{x\}$$ denoting the fractional part of $$x$$.

Which of the following is/are true?

$$A.$$ Range of $$f(x)=[0,1]$$

$$B.$$ The number of values of $$x$$ for which function is continuous but not differentiable is $$1$$.

$$C.$$ $$f(x)=1$$ has two solutions.

$$D.$$ Number of values of $$x$$ for which $$f(x)$$ is discontinuous is $$2$$ .

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