g(x)=(5-x)/(2x-1) f(x)= (x+5)/(2x+1) what is g(f(x))

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10-12-2017
Mathematics

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g(x)=(5-x)/(2x-1) f(x)= (x+5)/(2x+1) what is g(f(x))

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jdoe0001 jdoe0001 · Answer 1 · 2017-12-11T00:08:42+01:00

[tex]\bf \begin{cases} g(x)=\cfrac{5-x}{2x-1}\\\\ f(x)=\cfrac{x+5}{2x+1} \end{cases}\qquad g(~~f(x)~~)=\cfrac{5-f(x)}{2[f(x)]+1} \\\\\\ g(~~f(x)~~)=\cfrac{5-\left(\frac{x+5}{2x+1} \right)}{2\left(\frac{x+5}{2x+1} \right)-1}\implies g(~~f(x)~~)=\cfrac{\frac{5(2x+1)-(x+5)}{2x+1}}{\frac{2x+10}{2x+1}-1}[/tex]

[tex]\bf g(~~f(x)~~)=\cfrac{\frac{10x+5-x-5}{2x+1}}{\frac{2x+10-1(2x+1)}{2x+1}}\implies g(~~f(x)~~)=\cfrac{\frac{9x}{2x+1}}{\frac{2x+10-2x-1}{2x+1}} \\\\\\ g(~~f(x)~~)=\cfrac{\frac{9x}{2x+1}}{\frac{9}{2x+1}}\implies g(~~f(x)~~)=\cfrac{\underline{9} x}{\underline{2x+1}}\cdot \cfrac{\underline{2x+1}}{\underline{9}} \\\\\\ g(~~f(x)~~)=x[/tex]