if-g-5-f-5-g-5-f-5-1-then-f-4-g-4-f-4-1-when-is-Gis-a-I-function-and-F-is-a-constant-

Question Number 161666 by mathlove last updated on 21/Dec/21

$${if}\:\:\frac{{g}\left(\mathrm{5}\right){f}\left(\mathrm{5}\right)}{{g}\left(\mathrm{5}\right)+{f}\left(\mathrm{5}\right)}=\mathrm{1}\:\:\:{then}\frac{{f}\left(\mathrm{4}\right)+{g}\left(\mathrm{4}\right)}{{f}\left(\mathrm{4}\right)+\mathrm{1}}=? \\ $$$${when}\:{is}\:\:\:\:\:{Gis}\:{a}\:{I}\:{function}\:\:{and}\:{F}\:{is}\:{a}\:{constant} \\ $$

Commented by mr W last updated on 21/Dec/21

$${the}\:{language}\:{is}\:{not}\:{clear}. \\ $$$${what}\:{are}\:{G}\:{and}\:{F}? \\ $$$${what}\:{is}\:{a}\:{I}\:{function}? \\ $$

Commented by mathlove last updated on 21/Dec/21

$$ \\ $$$$ \\ $$$$ \\ $$g is a fixed subject and f is subject to objectivity

Commented by mathlove last updated on 21/Dec/21

$${g}\left({x}\right)={c} \\ $$$${f}\left({x}\right)={x} \\ $$

Commented by mathlove last updated on 21/Dec/21

$${pleas}\:{sir}\:\:\:{mrW} \\ $$

Answered by Rasheed.Sindhi last updated on 21/Dec/21

$$\frac{{g}\left(\mathrm{5}\right){f}\left(\mathrm{5}\right)}{{g}\left(\mathrm{5}\right)+{f}\left(\mathrm{5}\right)}=\frac{{c}.\mathrm{5}}{{c}+\mathrm{5}}=\mathrm{1}\Rightarrow\mathrm{5}{c}={c}+\mathrm{5}\Rightarrow{c}=\frac{\mathrm{5}}{\mathrm{4}} \\ $$$$\frac{{f}\left(\mathrm{4}\right)+{g}\left(\mathrm{4}\right)}{{f}\left(\mathrm{4}\right)+\mathrm{1}}=\frac{\mathrm{4}+{c}}{\mathrm{4}+\mathrm{1}}=\frac{\mathrm{4}+\frac{\mathrm{5}}{\mathrm{4}}}{\mathrm{5}}=\frac{\mathrm{21}}{\mathrm{4}×\mathrm{5}}=\frac{\mathrm{21}}{\mathrm{20}} \\ $$

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