Function f(x) = sin x + tan x + operatorname{ | vedclass

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(A) Given $f(x) = \sin x + 	an x + \operatorname{sgn}(x^2 - 6x + 10)$.First,analyze the term $x^2 - 6x + 10$. This can be written as $(x-3)^2 + 1$.Si

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Periodic with period $2\pi$

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(A) Given $f(x) = \sin x + 	an x + \operatorname{sgn}(x^2 - 6x + 10)$.First,analyze the term $x^2 - 6x + 10$. This can be written as $(x-3)^2 + 1$.Since $(x-3)^2 \ge 0$ for all real $x$,it follows that $(x-3)^2 + 1 \ge 1$.Because the argument of the signum function is always positive,$\operatorname{sgn}(x^2 - 6x + 10) = 1$ for all $x \in \mathbb{R}$.Thus,the function simplifies to $f(x) = \sin x + 	an x + 1$.The period of $\sin x$ is $2\pi$ and the period of $	an x$ is $\pi$.The fundamental period of the sum of periodic functions is the least common multiple of their individual periods.$	ext{LCM}(2\pi, \pi) = 2\pi$.Therefore,the function is periodic with period $2\pi$.

Function $f(x) = \sin x + \tan x + \operatorname{sgn}(x^2 - 6x + 10)$ is (where $\operatorname{sgn}$ is the signum function):

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