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Question Number 53161 by peter frank last updated on 18/Jan/19

Answered by peter frank last updated on 18/Jan/19

from  x_(n+1 ) =(1/r)[(r−1)x_n +Ax_(n ) ^(1−r) ]  three iteration  n=0,1,2  A=10  x_0 =2.0

$${from} \\ $$$${x}_{{n}+\mathrm{1}\:} =\frac{\mathrm{1}}{{r}}\left[\left({r}−\mathrm{1}\right){x}_{{n}} +{Ax}_{{n}\:} ^{\mathrm{1}−{r}} \right] \\ $$$${three}\:{iteration} \\ $$$${n}=\mathrm{0},\mathrm{1},\mathrm{2} \\ $$$${A}=\mathrm{10} \\ $$$${x}_{\mathrm{0}} =\mathrm{2}.\mathrm{0} \\ $$$$ \\ $$

Answered by peter frank last updated on 18/Jan/19

2) from  x_(n+1) =x_n (2−Ax_(n ) )  three iteration  n=0,1,2  A=7  x_0 =?

$$\left.\mathrm{2}\right)\:{from} \\ $$$${x}_{{n}+\mathrm{1}} ={x}_{{n}} \left(\mathrm{2}−{Ax}_{{n}\:} \right) \\ $$$${three}\:{iteration} \\ $$$${n}=\mathrm{0},\mathrm{1},\mathrm{2} \\ $$$${A}=\mathrm{7} \\ $$$${x}_{\mathrm{0}} =? \\ $$$$ \\ $$

Answered by peter frank last updated on 18/Jan/19

i)fog[oh(x)]=[fog]oh(x)  fog(x)=f[g(x)]  gof (x)=g[f(x)]    ii)find   fogoh(x)] and then interchange  to get inverse

$$\left.{i}\right){fog}\left[{oh}\left({x}\right)\right]=\left[{fog}\right]{oh}\left({x}\right) \\ $$$${fog}\left({x}\right)={f}\left[{g}\left({x}\right)\right] \\ $$$${gof}\:\left({x}\right)={g}\left[{f}\left({x}\right)\right] \\ $$$$ \\ $$$$\left.{ii}\right){find}\: \\ $$$$\left.{fogoh}\left({x}\right)\right]\:{and}\:{then}\:{interchange} \\ $$$${to}\:{get}\:{inverse} \\ $$

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