1. If $\displaystyle f\left(x\right)={{1}\over{x^2-16}}$ and $g(x)=\displaystyle \sqrt{x}$, then the domain of $f$ composite $g$, $(f \circ g)(x)$, is

    All real numbers

    $\left\{x\,\left\vert\,x\ge0,\, x \in (-\infty,\infty)\right.\rigth\}$

    $\displaystyle (-\infty, -4) \cup (4, \infty)$

    $(0, 4) \cup ( 4,\infty)$ $\displaystyle \left\{x\,\left\vert\,x\neq 16, x \mbox{ is a nonnegative real number}\right.\right\}$

  2. $\displaystyle \frac{ \cos \theta} { \sin \theta\, } = -\tan(\theta -\pi/2) $ is an identity and is true for all values of $\theta$ in the set

    $\displaystyle\left\{\theta \,\left\vert\, \theta \neq {{\pi\,n}\over{2}} ,\,n \mbox{ is an integer},\, \theta \in (-\infty,\infty)\right.\right\}$

    $\displaystyle\left\{\theta \,\left\vert\, \theta \neq \pi\,n ,\,n \mbox{ is an integer},\, \theta \in (-\infty,\infty)\right.\right\}$

    $\displaystyle\left\{\theta \,\left\vert\, -\infty < \theta < \infty \right.\right\}$

    $\displaystyle\left\{\theta \,\left\vert\, \theta \neq {{\pi\,\left(2\,n+1\r... ...{2}} ,\,n \mbox{ is an integer},\, \theta \in (-\infty,\infty)\right.\right\}$

    $(0,2\pi)$


Department of Mathematics
Last modified: 2026-07-11