Question

Given domain sine x restricted to [-pi/2, pi/2 ], define domain and range of sin (x + pi/4 )

Answer 1

well, it must be that
x+pi/4 is within this boundary [-pi/2 , pi/2]
Meaning
\[\Large -\frac{\pi}{2}\le x+\frac\pi4\le\frac\pi2\]And just manipulate :)