Question and Answers Forum

All Questions      Topic List

Trigonometry Questions

Previous in All Question      Next in All Question      

Previous in Trigonometry      Next in Trigonometry      

Question Number 143959 by bobhans last updated on 20/Jun/21

$$\mathrm{If}\mathrm{g}\left(\mathrm{x}\right)={(4\cos {}^4\mathrm{x}-2\cos 2\mathrm{x}-\frac{1}{2}\cos 4\mathrm{x}-{\mathrm{x}}^7)}^{\frac{1}{7}}$$$$\mathrm{then}\mathrm{tbe}\mathrm{value}\mathrm{of}\mathrm{g}\left(\mathrm{g}\left(100\right)\right)\mathrm{is}$$$$\mathrm{equal}\mathrm{to}...$$

Answered by Olaf_Thorendsen last updated on 20/Jun/21

$$\mathrm{X}={4\cos }^{4}x-2\cos 2x-\frac{1}{2}\cos 4x$$$$\mathrm{X}=4{\left(\frac{1+\cos 2x}{2}\right)}^2-2\cos 2x-\frac{1}{2}({2\cos }^{2}2x-1)$$$$\mathrm{X}=\frac{3}{2}$$$$g\left(x\right)={(\mathrm{X}-x^7)}^{\frac{1}{7}}$$$$g\left(x\right)={(\frac{3}{2}-x^7)}^{\frac{1}{7}}$$$$g\left(100\right)={(\frac{3}{2}-{100}^7)}^{\frac{1}{7}}$$$$g\mathrm{o}g\left(100\right)={(\frac{3}{2}-g{\left(100\right)}^7)}^{\frac{1}{7}}$$$$g\mathrm{o}g\left(100\right)={(\frac{3}{2}-(\frac{3}{2}-{100}^7))}^{\frac{1}{7}}$$$$g\mathrm{o}g\left(100\right)=100$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com