the function m is given by m(x) = tan(x + π/2) all input values in the domain of m that yield an output…

Explanation:

Step1: Set up the equation

Set $\tan(x + \frac{\pi}{2})=\sqrt{3}$.

Step2: Recall the tangent - inverse relationship

We know that if $\tan\theta=\sqrt{3}$, then $\theta=\frac{\pi}{3}+k\pi$, where $k\in\mathbb{Z}$. So $x+\frac{\pi}{2}=\frac{\pi}{3}+k\pi$.

Step3: Solve for x

Subtract $\frac{\pi}{2}$ from both sides: $x=\frac{\pi}{3}-\frac{\pi}{2}+k\pi$. Calculate $\frac{\pi}{3}-\frac{\pi}{2}=\frac{2\pi - 3\pi}{6}=-\frac{\pi}{6}$. So $x =-\frac{\pi}{6}+k\pi,k\in\mathbb{Z}$.

Answer:

$x =-\frac{\pi}{6}+k\pi,k\in\mathbb{Z}$