y-log-2-sin-x-cos-x-R-y-Range-

Question Number 205107 by mnjuly1970 last updated on 08/Mar/24

y = {l o g}_{2} (s i n (x) + c o s (x))

\Rightarrow R_{y} = ? (R a n g e)

Commented by mr W last updated on 08/Mar/24

2^{- \infty} = 0 < \sin x + \cos x ⩽ \sqrt{2} = 2^{\frac{1}{2}}

- \infty < \log_{2} (\sin x + \cos x) ⩽ \frac{1}{2}

i . e . R_{y} = (- \infty, \frac{1}{2}]

Commented by mnjuly1970 last updated on 08/Mar/24

g r a t e f u l s i r W