Which of the following functions is a monoton | vedclass

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(D) Let us analyze each function:$1$. For $f(x) = x + |x|$:If $x \ge 0$,$f(x) = x + x = 2x$,which is increasing.If $x < 0$,$f(x) = x - x = 0$,which is

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All of the above

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(D) Let us analyze each function:$1$. For $f(x) = x + |x|$:If $x \ge 0$,$f(x) = x + x = 2x$,which is increasing.If $x Thus,$f(x)$ is monotonically increasing.$2$. For $f(x) = x - |x|$:If $x \ge 0$,$f(x) = x - x = 0$,which is constant.If $x Thus,$f(x)$ is monotonically increasing.$3$. For $f(x) = x|x|$:If $x \ge 0$,$f(x) = x^2$,which is increasing for $x \ge 0$.If $x Since the derivative $f'(x) = 2|x| \ge 0$ for all $x$,it is monotonically increasing.Since all three functions are monotonically increasing,the correct option is $D$.

Which of the following functions is a monotonically increasing function?

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