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Question Number 105593 by Study last updated on 30/Jul/20

f(x)=(((√(2x+1))×(√(2x+1)))/(2x+1))      Dom_f =?

$${f}\left({x}\right)=\frac{\sqrt{\mathrm{2}{x}+\mathrm{1}}×\sqrt{\mathrm{2}{x}+\mathrm{1}}}{\mathrm{2}{x}+\mathrm{1}}\:\:\:\:\:\:{Dom}_{{f}} =? \\ $$

Answered by mathmax by abdo last updated on 30/Jul/20

D_f =]−(1/2),+∞[

$$\left.\mathrm{D}_{\mathrm{f}} =\right]−\frac{\mathrm{1}}{\mathrm{2}},+\infty\left[\right. \\ $$

Commented by Study last updated on 30/Jul/20

why show u practice

$${why}\:{show}\:{u}\:{practice} \\ $$

Answered by mathmax by abdo last updated on 30/Jul/20

what practice here ?   x∈ Df ⇔ 2x+1 ≥0 and 2x+1 ≠0 ⇒2x+1>0 ⇒  x>−(1/2) ⇒D_f =]−(1/2),+∞[

$$\mathrm{what}\:\mathrm{practice}\:\mathrm{here}\:?\:\:\:\mathrm{x}\in\:\mathrm{Df}\:\Leftrightarrow\:\mathrm{2x}+\mathrm{1}\:\geqslant\mathrm{0}\:\mathrm{and}\:\mathrm{2x}+\mathrm{1}\:\neq\mathrm{0}\:\Rightarrow\mathrm{2x}+\mathrm{1}>\mathrm{0}\:\Rightarrow \\ $$$$\left.\mathrm{x}>−\frac{\mathrm{1}}{\mathrm{2}}\:\Rightarrow\mathrm{D}_{\mathrm{f}} =\right]−\frac{\mathrm{1}}{\mathrm{2}},+\infty\left[\right. \\ $$

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