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Question Number 107674 by Study last updated on 12/Aug/20

f (x) = \sqrt{x} \sqrt{x} D_{f} = ? ? ?

Answered by Her_Majesty last updated on 12/Aug/20

x = {r e}^{i θ}; r \in R^{+} \land θ \in R

\Rightarrow

f (x) = \sqrt{{r e}^{i θ}} \sqrt{{r e}^{i θ}} = \sqrt{r} e^{i θ / 2} \sqrt{r} e^{i θ / 2} = {r e}^{i θ} = x

Answered by Her_Majesty last updated on 12/Aug/20

x ⩾ 0 \Rightarrow f (x) = x

x < 0 \Rightarrow f (x) = i \sqrt{- x} \times i \sqrt{- x} = - 1 (- x) = x

\Rightarrow f (x) = x

Commented by Study last updated on 12/Aug/20

w h a t i s t h e d o m a i n o f f (x) ?

Commented by Her_Majesty last updated on 12/Aug/20

i f w e s t a y i n R t h e d o m a i n i s x ⩾ 0