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let-f-x-x-and-g-x-x-find-the-domain-of-f-g-x-help-me-sir-




Question Number 93844 by mhmd last updated on 15/May/20
let f(x)=(√x)  and g(x)=(√x) find the domain of (f.g)(x) ?  help me sir
$${let}\:{f}\left({x}\right)=\sqrt{{x}}\:\:{and}\:{g}\left({x}\right)=\sqrt{{x}}\:{find}\:{the}\:{domain}\:{of}\:\left({f}.{g}\right)\left({x}\right)\:? \\ $$$${help}\:{me}\:{sir} \\ $$
Answered by  M±th+et+s last updated on 15/May/20
(f.g)(x)=f((√x))=(√(√x)) so domain and range are [0,∞)
$$\left({f}.{g}\right)\left({x}\right)={f}\left(\sqrt{{x}}\right)=\sqrt{\sqrt{{x}}}\:{so}\:{domain}\:{and}\:{range}\:{are}\:\left[\mathrm{0},\infty\right) \\ $$$$ \\ $$
Commented by  M±th+et+s last updated on 15/May/20
  the range  we know that 0≤(√x)≤∞.......(√)                              (√0)≤(√(√x))<(√∞)                                0≤f(x)<∞
$$ \\ $$$${the}\:{range} \\ $$$${we}\:{know}\:{that}\:\mathrm{0}\leqslant\sqrt{{x}}\leqslant\infty…….\sqrt{} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\sqrt{\mathrm{0}}\leqslant\sqrt{\sqrt{{x}}}<\sqrt{\infty} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{0}\leqslant{f}\left({x}\right)<\infty \\ $$$$ \\ $$$$ \\ $$

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