Question Number 84728 by mr W last updated on 15/Mar/20
![y=x[x[x]] with x∈R^+ find the range of function and solve x[x[x]]=150.](https://www.tinkutara.com/question/Q84728.png)
$${y}={x}\left[{x}\left[{x}\right]\right]\:{with}\:{x}\in{R}^{+} \\ $$$${find}\:{the}\:{range}\:{of}\:{function} \\ $$$${and}\:{solve}\:{x}\left[{x}\left[{x}\right]\right]=\mathrm{150}. \\ $$
Commented by MJS last updated on 16/Mar/20
Commented by MJS last updated on 16/Mar/20
$$\mathrm{this}\:\mathrm{is}\:\mathrm{my}\:\mathrm{work}\:\mathrm{to}\:\mathrm{an}\:\mathrm{earlier}\:\mathrm{question}.\:\mathrm{I}\:\mathrm{never} \\ $$$$\mathrm{posted}\:\mathrm{it}\:\mathrm{before} \\ $$
Commented by mr W last updated on 16/Mar/20
$${thank}\:{you}\:{sir}!\:{that}'{s}\:{perfect}. \\ $$
Commented by MJS last updated on 16/Mar/20
![I started trying the next stage x[x[x[x]]] but it′s getting very complex](https://www.tinkutara.com/question/Q84787.png)
$$\mathrm{I}\:\mathrm{started}\:\mathrm{trying}\:\mathrm{the}\:\mathrm{next}\:\mathrm{stage} \\ $$$${x}\left[{x}\left[{x}\left[{x}\right]\right]\right] \\ $$$$\mathrm{but}\:\mathrm{it}'\mathrm{s}\:\mathrm{getting}\:\mathrm{very}\:\mathrm{complex} \\ $$
Commented by mr W last updated on 16/Mar/20
$${that}'{s}\:{true}\:{sir}! \\ $$
Commented by M±th+et£s last updated on 16/Mar/20
$${i}\:{think}\:{there}\:{is}\:{a}\:{typo} \\ $$$${if}\:{i}=\mathrm{2}\:{k}=\mathrm{1}\:\:\mathrm{10}\leqslant{n}\leqslant\mathrm{15} \\ $$
Commented by M±th+et£s last updated on 16/Mar/20
$${and} \\ $$$$\mathrm{27}\leqslant{n}\leqslant\mathrm{30} \\ $$
Commented by MJS last updated on 16/Mar/20
![you are wrong because also q=i^2 +k and (k/i)≤f<((k+1)/i) try it, you cannot get 10, 11, 12 as solution it′s not easy to understand the jumps of y=x[x[x]]](https://www.tinkutara.com/question/Q84818.png)
$$\mathrm{you}\:\mathrm{are}\:\mathrm{wrong}\:\mathrm{because}\:\mathrm{also} \\ $$$${q}={i}^{\mathrm{2}} +{k} \\ $$$$\mathrm{and} \\ $$$$\frac{{k}}{{i}}\leqslant{f}<\frac{{k}+\mathrm{1}}{{i}} \\ $$$$\mathrm{try}\:\mathrm{it},\:\mathrm{you}\:\mathrm{cannot}\:\mathrm{get}\:\mathrm{10},\:\mathrm{11},\:\mathrm{12}\:\mathrm{as}\:\mathrm{solution} \\ $$$$\mathrm{it}'\mathrm{s}\:\mathrm{not}\:\mathrm{easy}\:\mathrm{to}\:\mathrm{understand}\:\mathrm{the}\:\mathrm{jumps}\:\mathrm{of} \\ $$$${y}={x}\left[{x}\left[{x}\right]\right] \\ $$