Question

Solve $f\left(x\right)={\log }_2(\sin (x-\frac{\pi }{4})+3)$. Find range of $f\left(x\right)$

Answer 1

$-1\le \sin (x-\frac{\pi }{4})$

$f\left(x\right)={\log }_2(\sin (x-\frac{\pi }{4})+3)$

Max. value

$={\log }_2(1+3)$

$={\log }_2\left(4\right)$

$=2$

Min. value

$={\log }_2(-1+3)$

$={\log }_2\left(2\right)$

$=1$

Range of $f\left(x\right)$ is $[1,2]$