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Question Number 204273 by mustafazaheen last updated on 10/Feb/24

$$\mathrm{f}\left(\mathrm{x}\right)=\frac{1}{{(\mathrm{x}-1)}^{\ln \left(\frac{2}{4}\right)}}$$$$\mathrm{Domain}\mathrm{f}\left(\mathrm{x}\right)=?$$

Answered by Mathspace last updated on 11/Feb/24

$$f\left(x\right)=\frac{1}{{(x-1)}^{ln\left(\frac{1}{2}\right)}}=\frac{1}{{(x-1)}^{-ln2}}$$$$={(x-1)}^{ln2}=e^{ln2ln(x-1)}\Rightarrow$$$$D_f=]1,+\mathrm{\infty }[engeneral$$$$lafonctionx\to x^{a}estdefinie$$$$pourx>0\left(surR\right)$$

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