OG详解-OG7 数学1 Q36

Choice C is correct. It’s given that the function f is defined by f(x) = |x-4x|. It’s also given that f(5)-f(a)=-15. Substituting 5 for x in the function f(x) =  |x-4x|  yields f(5) = |5-4(5)| and substituting a for x in the function f(x) = | x-4x |  yields f(a) =| a-4a |. Therefore, f(5) = 15 and f(a) =-3a. Substituting 15 for f(5) and |-3a| for f(a) in the equation f(5)-f(a) = -15 yields 15- |-3a | =-15. Subtracting 15 from both sides of this equation yields - |-3a | = -30. Dividing both sides of this equation by -1yields  |-3a| = 30. By the definition of absolute value, if |-3a| = 30, then -3a = 30 or -3a = -30. Dividing both sides of each of these equations by -3 yields a = -10 or a = 10, respectively. Thus, of the given choices, a value of a that satisfies f(5)-f(a) = -15 is 10.
Choice A is incorrect and may result from conceptual or calculation errors. Choice B is incorrect and may result from conceptual or calculation errors. Choice D is incorrect and may result from conceptual or calculation errors.