Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 165153 by mathlove last updated on 26/Jan/22

$$f\left(x\right)=3e^{2x}$$$$f^{-1}\left(x\right)=?$$

Answered by mahdipoor last updated on 26/Jan/22

$$\Rightarrow x=3e^{2y}\Rightarrow \frac{1}{2}ln\frac{x}{3}=y=f^{-1}\left(x\right)$$

Answered by MathsFan last updated on 27/Jan/22

$$lety=3e^{2x}$$$$x=3e^{2y}\to logx=2ylog3e$$$$\to 2y={log}_{3e}x\to y=\frac{{log}_{3e}x}{2}$$$$f^{-1}\left(x\right)=\frac{{log}_{3e}x}{2}$$$$$$

Answered by alephzero last updated on 28/Jan/22

$$f\left(x\right)=3e^{2x}$$$$f^{-1}\left(x\right)=?$$$$x=3e^{2y}$$$$\Rightarrow \frac{x}{3}=e^{2y}$$$$\Rightarrow \ln \frac{x}{3}=2y$$$$\Rightarrow \frac{\ln \frac{x}{3}}{2}=\frac{\ln x-\ln 3}{2}=y$$$$\Rightarrow f^{-1}\left(x\right)=\frac{\ln x-\ln 3}{2}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com