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Snowcat [4.5K]
3 years ago
8

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

Mathematics
1 answer:
Elina [12.6K]3 years ago
3 0
\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}

\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
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