Which of the following functions is a strictl | vedclass

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(D) Let us analyze each function:$A) f(x) = x + |x| = \begin{cases} 2x, & x \ge 0 \ 0, & x < 0 \end{cases}$. This is not strictly increasing because

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$f(x) = x|x|$

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(D) Let us analyze each function:$A) f(x) = x + |x| = \begin{cases} 2x, & x \ge 0 \ 0, & x $B) f(x) = x - |x| = \begin{cases} 0, & x \ge 0 \ 2x, & x $C) f(x) = [x]$ (Greatest Integer Function). This is a step function and is not strictly increasing as it remains constant between integers.$D) f(x) = x|x| = \begin{cases} x^2, & x \ge 0 \ -x^2, & x For $x_1 < x_2$,if both are positive,$x_1^2 < x_2^2$. If both are negative,$-x_1^2 < -x_2^2$. If $x_1 < 0$ and $x_2 \ge 0$,then $f(x_1) < 0$ and $f(x_2) \ge 0$,so $f(x_1) < f(x_2)$. Thus,$f(x)$ is strictly increasing.

Which of the following functions is a strictly increasing function?

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