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LekaFEV [45]
3 years ago
11

Mixed numbers from 0-2 with intervals of 1/3

Mathematics
1 answer:
prisoha [69]3 years ago
5 0
0, 1/3, 2/3, 1, 1 1/3, 1 2/3, 2
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\bf \begin{cases}
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\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}

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g(~~f(x)~~)=\cfrac{\frac{9x}{2x+1}}{\frac{2x+10-2x-1}{2x+1}}
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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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