The function f(x) = tan x - x is: | vedclass

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(C) Given the function $f(x) = 	an x - x$. To determine the nature of the function,we find its derivative with respect to $x$: $f'(x) = \frac{d}{dx}(

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Never decreases

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(C) Given the function $f(x) = 	an x - x$. To determine the nature of the function,we find its derivative with respect to $x$: $f'(x) = \frac{d}{dx}(	an x - x) = \sec^2 x - 1$. Using the trigonometric identity $1 + 	an^2 x = \sec^2 x$,we get: $f'(x) = 	an^2 x$. Since the square of any real number is always non-negative,$	an^2 x \ge 0$ for all $x$ in the domain of $	an x$. Because $f'(x) \ge 0$ for all $x$,the function $f(x)$ is a monotonically increasing function,which means it never decreases.

The function $f(x) = \tan x - x$ is:

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