91Ó°ÊÓ

An absolute value function is a function that contains an algebraic expression with in absolute value symbols

For option A) $f\left(x\right)=2x$

Put $x=-\frac{1}{2}$into the given function

$\begin{array}{l}f\left(x\right)=2(−\frac{1}{2})\\ f\left(x\right)=−1\end{array}$

Hence, value of function is

$f(−\frac{1}{2})=−1.$

Therefore, option (A) is not correct.

For option B)

Put $x=-\frac{1}{2}$into$f\left(x\right)=\left|-2x\right|$

$\begin{array}{l}f\left(x\right)=|−2(−\frac{1}{2})|\\ f\left(x\right)=\left|1\right|\\ f\left(x\right)=1\end{array}$

Hence, value of function is$f\left(-\frac{1}{2}\right)≠-1.$

Therefore, option (B) is correct.

For (C)$f\left(x\right)=\left[\left[x\right]\right]$

Put $x=-\frac{1}{2}$into the given function

$\begin{array}{l}f\left(x\right)=\left[\text{​}\left[x\right]\text{​}\right]\\ f\left(x\right)=\left[\text{​}[−\frac{1}{2}]\text{​}\right]\\ f\left(x\right)=−1\end{array}$

Therefore, option (C) is incorrect.

For (D) $f\left(x\right)=\left[\left[2x\right]\right]$

Put $x=-\frac{1}{2}$into the given function

$\begin{array}{l}f\left(x\right)=\left[\text{​}\left[2x\right]\text{​}\right]\\ f\left(x\right)=\left[\text{​}\left[2(−\frac{1}{2})\right]\text{​}\right]\\ f\left(x\right)=−1\end{array}$

Therefore, option (D) is incorrect.

Hence, value of function is $f\left(-\frac{1}{2}\right)=-1.$

Therefore, option (D) is not correct