The functions f and g are defined by the given equations, where x ≥ 0 . Which of the following

Question

The functions f and g are defined by the given equations, where x &#8805; 0 . Which of the following equations displays, as a constant or coefficient, the maximum value of the function it defines, where x &#8805; 0 ? f x = 18 ( 1.25 ) x + 41 g x = 9 0.73 x

Accepted Answer

Choice B is correct. For the function f , since the base of the exponent, 1.25 , is greater than 1 , the value of 1.25 x increases as x increases. Therefore, the value of 18 1.25 x and the value of 18 1.25 x + 41 also increase as x increases. Since f is therefore an increasing function where x &ge; 0 , the function f has no maximum value. For the function g , since the base of the exponent, 0.73 , is less than 1 , the value of 0.73 x decreases as x increases. Therefore, the value of 9 0.73 x also decreases as x increases. It follows that the maximum value of g x for x &ge; 0 occurs when x = 0 . Substituting 0 for x in the function g yields g 0 = 9 0.73 0 , which is equivalent to g 0 = 9 1 , or g 0 = 9 . Therefore, the maximum value of g x for x &ge; 0 is 9 , which appears as a coefficient in equation II. So, of the two equations given, only Iwe displays, as a constant or coefficient, the maximum value of the function it defines, where x &ge; 0 . Choice A is incorrect and may result from conceptual or calculation errors. Choice C is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.

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