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Question Number 114152 by mohammad17 last updated on 17/Sep/20

$$iff\left(x\right)=3x-2find{f}^{-1}\left(x\right)?$$$$$$$$\left(2\right)iff\left(x\right)=3x^2-x+10,g\left(x\right)=1-20xfind$$$$\left(fog\right)\left(5\right)$$

Answered by bemath last updated on 17/Sep/20

$$f^{-1}\left(x\right)=\frac{x+2}{3}$$$$f\left(g\left(5\right)\right)=f(-99)=3{(-99)}^2+99+10$$

Commented by mohammad17 last updated on 17/Sep/20

$$thankyousir$$

Answered by physicstutes last updated on 17/Sep/20

$$\left(1\right)f\left(x\right)=3x-2$$$$\mathrm{let}f\left(x\right)=u$$$$\Rightarrow u=3x-2$$$$u+2=3x$$$$\mathrm{and}x=\frac{u+2}{3}$$$$\therefore f^{-1}\left(x\right)=\frac{x+2}{3}.$$$$\left(2\right)f\left(x\right)=3x^2-x+10\mathrm{and}\mathrm{g}\left(x\right)=1-20x$$$$f_o\mathrm{g}\left(5\right)=f\left[\mathrm{g}\left(5\right)\right]$$$$\mathrm{but}\mathrm{g}\left(5\right)=1-20\left(5\right)=1-100=-99.$$$$\Rightarrow f_o\mathrm{g}\left(5\right)=f(-99)$$$$\mathrm{and}f(-99)=3{(-99)}^2-(-99)+10=3(970,299)+99+10$$$$-------------------------------$$$$\left(1\right)f^{-1}\left(x\right)=\frac{x+2}{3},\left(2\right)f{}_o\mathrm{g}\left(5\right)=2,910,997$$

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