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Question Number 82078 by jagoll last updated on 18/Feb/20

$$f\left({10}^x\right)=\sqrt{x}$$$$whatis{f}^{-1}\left(x\right)=?$$

Commented by john santu last updated on 18/Feb/20

$$hahaha..ithinkyoucansolvethis$$$$problem$$

Answered by Kunal12588 last updated on 18/Feb/20

$${10}^x=t$$$$\Rightarrow xlog10=logt$$$$\Rightarrow x=\frac{logt}{log10}={log}_{10}t$$$$f\left(t\right)=\sqrt{{log}_{10}t}$$$$\Rightarrow t={10}^{{\left(f\left(t\right)\right)}^2}$$$$f^{-1}\left(t\right)={10}^{t^2}$$$$\Rightarrow f^{-1}\left(x\right)={10}^{x^2}$$

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