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