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3 years ago

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

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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Step-by-step explanation:

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Let's compare the expressions in the given options to the value we got above:

Option 1: 3*3⁶

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Option 2: 3⁷ ÷ 3⁰

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$\frac{1}{27} * \frac{1}{81}$ (changing from division to multiplication)

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