If-f-x-defined-over-the-domain-0-1-then-domain-of-function-f-10-x-is-

Question Number 13808 by Tinkutara last updated on 23/May/17

$$\mathrm{If}\:{f}\left({x}\right)\:\mathrm{defined}\:\mathrm{over}\:\mathrm{the}\:\mathrm{domain}\:\left[\mathrm{0},\:\mathrm{1}\right] \\ $$$$\mathrm{then}\:\mathrm{domain}\:\mathrm{of}\:\mathrm{function}\:{f}\left(\mathrm{10}^{{x}} \right)\:\mathrm{is}? \\ $$

Answered by ajfour last updated on 23/May/17

$${then}\:{x}\leqslant\mathrm{0}\: \\ $$$$\mathrm{0}\leqslant\mathrm{10}^{{x}} \leqslant\mathrm{1} \\ $$$${taking}\:{logarithm} \\ $$$${this}\:{implies}, \\ $$$$−\infty<{x}\leqslant\mathrm{0} \\ $$$$ \\ $$

Commented by Tinkutara last updated on 23/May/17

$$\mathrm{OK}.\:\mathrm{Thanks}! \\ $$

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