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Question Number 129759 by mohammad17 last updated on 18/Jan/21

$$sincef\left(z\right)=\sqrt{z-1}find{f}^{-1}\left(z\right)?$$

Answered by I want to learn more last updated on 18/Jan/21

$$\mathrm{y}=\sqrt{\mathrm{z}-1}$$$${\mathrm{y}}^2=\mathrm{z}-1$$$${\mathrm{y}}^2+1=\mathrm{z}$$$$\mathrm{z}={\mathrm{y}}^2+1$$$${\mathrm{f}}^{-1}\left(\mathrm{z}\right)={\mathrm{z}}^2+1$$

Commented by Olaf last updated on 18/Jan/21

$$\mathrm{only}\mathrm{for}z⩾0\mathrm{sir}.$$$${\mathcal{D}}_f=[1;+\mathrm{\infty }[\mathrm{and}{\mathcal{D}}_{f^{-1}}=[0;+\mathrm{\infty }[$$

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