9. If the function g is defined by g (x) = x/(x+1)', which of the following is true?
Answer: A
g(10) < g(20)
The function g(x) = x/(x+1) is an increasing function for x ≥ 0, which means that as the input value increases, the output value also increases. Therefore, it is true that g(10) is less than g(20).
A) g(10) < g(20)
This option is correct because g(x) is a monotonically increasing function for non-negative values of x. Evaluating g(10) and g(20), we find that g(10) = 10/11 and g(20) = 20/21, and since 10/11 < 20/21, this statement holds true.
B) g(20) < g(10)
This option is incorrect as it contradicts the property of the function g(x). Since g(x) is increasing, g(20) cannot be less than g(10); instead, it is greater.
C) g(0) = 1
This option is incorrect because when evaluating g(0), we have g(0) = 0/(0+1) = 0. Thus, g(0) does not equal 1.
D) g(1) = 0
This option is also incorrect. Evaluating g(1) gives us g(1) = 1/(1+1) = 1/2, which is clearly not equal to 0.
Conclusion
The correct answer is A) g(10) < g(20), as it accurately reflects the behavior of the function g(x) being an increasing function for x ≥ 0. All other options fail to correctly represent the values of g at specified points, demonstrating a misunderstanding of the function's properties.