# 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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