Question Number 209450 by RoseAli last updated on 10/Jul/24
Answered by Spillover last updated on 10/Jul/24
![f(x)=3x^2 g(x)=(√(x−2)) (fog)(x)=? (gof)(x)=? fog(x)=f[g(x)] fog(x)=f[(√(x−2)) ]=3(x−2)=3x−6 fog(x)=3x−6 gof(x)=g[f(x)] gof(x)=g[3x^2 ]=(√(3x^2 −2)) gof(x)=(√(3x^2 −2))](https://www.tinkutara.com/question/Q209451.png)
$${f}\left({x}\right)=\mathrm{3}{x}^{\mathrm{2}} \\ $$$${g}\left({x}\right)=\sqrt{{x}−\mathrm{2}} \\ $$$$\left({fog}\right)\left({x}\right)=? \\ $$$$\left({gof}\right)\left({x}\right)=? \\ $$$${fog}\left({x}\right)={f}\left[{g}\left({x}\right)\right] \\ $$$$\:{fog}\left({x}\right)={f}\left[\sqrt{{x}−\mathrm{2}}\:\right]=\mathrm{3}\left({x}−\mathrm{2}\right)=\mathrm{3}{x}−\mathrm{6} \\ $$$$\:{fog}\left({x}\right)=\mathrm{3}{x}−\mathrm{6} \\ $$$${gof}\left({x}\right)={g}\left[{f}\left({x}\right)\right] \\ $$$${gof}\left({x}\right)={g}\left[\mathrm{3}{x}^{\mathrm{2}} \right]=\sqrt{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{2}}\: \\ $$$${gof}\left({x}\right)=\sqrt{\mathrm{3}{x}^{\mathrm{2}} −\mathrm{2}}\: \\ $$$$ \\ $$