find-the-range-and-domain-of-f-x-f-x-sin-1-ln-x-10-

Question Number 68546 by aliesam last updated on 13/Sep/19

f i n d t h e r a n g e a n d d o m a i n o f f (x)

f (x) = \sqrt{{s i n}^{- 1} (l n \frac{x}{10})}

Answered by MJS last updated on 13/Sep/19

\sqrt{u} \in R \Rightarrow u ⩾ 0

\arcsin v \in R \Rightarrow - 1 ⩽ v ⩽ 1

\sqrt{\arcsin v} \in R \Rightarrow 0 ⩽ v ⩽ 1

0 ⩽ \ln \frac{x}{10} ⩽ 1 \Rightarrow 10 ⩽ x ⩽ 10 e

domain : 10 ⩽ x ⩽ 10 e

range : 0 ⩽ y ⩽ \frac{π}{\sqrt{2}}

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