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Question Number 180391 by Shrinava last updated on 11/Nov/22

$$\mathrm{y}=\mathrm{x}-\frac{2}{\mathrm{x}}$$$$\mathrm{Find}\mathrm{the}\mathrm{set}\mathrm{of}\mathrm{values}\mathrm{of}\mathrm{the}\mathrm{function}.$$

Commented by Shrinava last updated on 11/Nov/22

$$\mathrm{Answer}:(-\mathrm{\infty };+\mathrm{\infty })$$

Answered by aleks041103 last updated on 12/Nov/22

$$x\in \mathbb{R}\Rightarrow \mathrm{\forall }y\in I,\mathrm{\exists }x\in \mathbb{R},y=x-\frac{2}{x}$$$$\Rightarrow x^2-yx-2=0$$$$forthistohaveasolninthe\mathbb{R}:$$$$D=y^2-4\left(1\right)(-2)=y^2+8>0\iff y\in \mathbb{R}$$$$\Rightarrow ans.I=(-\mathrm{\infty },+\mathrm{\infty })\equiv \mathbb{R}$$$$$$

Commented by Shrinava last updated on 12/Nov/22

$$\mathrm{thank}\mathrm{you}\mathrm{dear}\mathrm{professor}$$

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