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Question Number 165870 by neinhaltsieger last updated on 09/Feb/22

$$$$$$\mathbf{f}({\mathbf{x}}^2-3)=\sqrt{\mathbf{x}-5},\mathbf{f}\left(\sqrt{21}\right)=?$$$$$$

Answered by eman_64 last updated on 09/Feb/22

$${\mathit{x}}^2-3=\mathit{y}\Rightarrow {\mathit{x}}^2=\mathit{y}+3$$$$\mathit{x}=\sqrt{\mathit{y}+3}$$$$\mathit{f}({\left(\sqrt{\mathit{x}+3}\right)}^2-3)=\sqrt{\sqrt{\mathit{x}+3}-5}$$$$\mathit{f}\left(\mathit{x}\right)=\sqrt{\sqrt{\mathit{x}+3}-5}$$$$\mathit{f}\left(\sqrt{21}\right)=\sqrt{\sqrt{\sqrt{21}+3}-5}$$$$$$

Commented by neinhaltsieger last updated on 12/Feb/22

$$Gracias$$

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