A Decreasing Function?

Calculus Level 3

True or False:

Consider the function $$f(x) = \dfrac{1}{x}$$. Since $$f'(x) = -\dfrac{1}{x^{2}} < 0$$, hence $$f(x)$$ is a decreasing function in its domain $$(-\infty, 0) \cup (0, \infty)$$.

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