Question Number 24747 by NECx last updated on 25/Nov/17
$${if}\:{f}\left({x}\right)=\mathrm{2}\mid{x}−\mathrm{3}\mid\:{and}\:{g}\left({x}\right)={x}^{\mathrm{2}} .{Find}: \\ $$$$\left({i}\right){gof}\:\left({ii}\right){fog}\:\left({iii}\right){domain}\:{of}\:{fog} \\ $$$$\left({iv}\right){range}\:{of}\:{gof} \\ $$$$ \\ $$
Answered by ajfour last updated on 25/Nov/17
![gof=g[f(x)]=4(x−3)^2 range ∈ [0, ∞) fog=f[g(x)]=2∣x^2 −3∣ domain ∈ (−∞, ∞) .](https://www.tinkutara.com/question/Q24749.png)
$${gof}={g}\left[{f}\left({x}\right)\right]=\mathrm{4}\left({x}−\mathrm{3}\right)^{\mathrm{2}} \\ $$$${range}\:\in\:\left[\mathrm{0},\:\infty\right) \\ $$$${fog}={f}\left[{g}\left({x}\right)\right]=\mathrm{2}\mid{x}^{\mathrm{2}} −\mathrm{3}\mid \\ $$$${domain}\:\in\:\left(−\infty,\:\infty\right)\:. \\ $$
Commented by NECx last updated on 25/Nov/17
$${thanks}\: \\ $$