Question

if the function ( g ) is defined by ( g(x)=\frac{x}{x + 1} ), which of the following is true?
( g(10)lt g(20) )
( g(20)lt g(10) )
( g(0)=1 )
( g(1)=0 )

Explanation:

Step1: Calculate \( g(10) \)

Substitute \( x = 10 \) into \( g(x)=\frac{x}{x + 1} \), we get \( g(10)=\frac{10}{10 + 1}=\frac{10}{11}\approx0.909 \).

Step2: Calculate \( g(20) \)

Substitute \( x = 20 \) into \( g(x)=\frac{x}{x + 1} \), we get \( g(20)=\frac{20}{20 + 1}=\frac{20}{21}\approx0.952 \).

Step3: Compare \( g(10) \) and \( g(20) \)

Since \( 0.909<0.952 \), we have \( g(10)<g(20) \).

Step4: Check \( g(0) \)

Substitute \( x = 0 \) into \( g(x) \), \( g(0)=\frac{0}{0 + 1}=0
eq1 \).

Step5: Check \( g(1) \)

Substitute \( x = 1 \) into \( g(x) \), \( g(1)=\frac{1}{1 + 1}=\frac{1}{2}
eq0 \).

Answer:

\( g(10) < g(20) \) (the first option)