The range of the real valued function f(x) = | vedclass

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Question

(B) Given the function $f(x) = \frac{1}{x - |x|}$.For $x \geq 0$, we have $|x| = x$, so the denominator $x - |x| = 0$. Thus, the function is undefined

Vedclass · Accepted Answer

$(-\infty, 0)$

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(B) Given the function $f(x) = \frac{1}{x - |x|}$.For $x \geq 0$, we have $|x| = x$, so the denominator $x - |x| = 0$. Thus, the function is undefined for $x \geq 0$.For $x Therefore, $f(x) = \frac{1}{2x}$ for $x As $x$ ranges from $(-\infty, 0)$, the value of $2x$ ranges from $(-\infty, 0)$.Consequently, the value of $\frac{1}{2x}$ ranges from $(-\infty, 0)$.Thus, the range of the function is $(-\infty, 0)$.

The range of the real valued function $f(x) = \frac{1}{x - |x|}$ is

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