Question and Answers Forum

All Questions      Topic List

Arithmetic Questions

Previous in All Question      Next in All Question      

Previous in Arithmetic      Next in Arithmetic      

Question Number 201952 by mathlove last updated on 16/Dec/23

$${\left(gof\right)}_x=2x-1$$$${\left(fog\right)}_x^{-1}=3x+2$$$${\left(fof\right)}_3=?$$

Answered by cortano12 last updated on 17/Dec/23

$$\{\begin{array}{l}(\mathrm{g}\circ \mathrm{f})\left(\mathrm{x}\right)=2\mathrm{x}-1\\ {(\mathrm{f}\circ \mathrm{g})}^{-1}\left(\mathrm{x}\right)=3\mathrm{x}+2\end{array}\Rightarrow (\mathrm{f}\circ \mathrm{f})\left(3\right)=?$$$$\left({(\mathrm{f}\circ \mathrm{g})}^{-1}(\mathrm{g}\circ \mathrm{f})\right)\left(\mathrm{x}\right)=(\mathrm{f}\circ \mathrm{f})\left(\mathrm{x}\right)=3(2\mathrm{x}-1)+2$$$$\iff (\mathrm{f}\circ \mathrm{f})\left(\mathrm{x}\right)=6\mathrm{x}-1$$$$\iff (\mathrm{f}\circ \mathrm{f})\left(3\right)=17$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com