The function f is defined by f ( x ) = | x - 4 x | . What value

Question

The function f is defined by f ( x ) = | x - 4 x | . What value of a satisfies f ( 5 ) - f ( a ) = - 15 ?

Accepted Answer

Choice C is correct. It's given that the function f is defined by f x = x - 4 x . It's also given that f 5 - f a = - 15 . Substituting 5 for x in the function f x = x - 4 x yields f 5 = 5 - 4 5 and substituting a for x in the function f x = x - 4 x yields f a = a - 4 a . Therefore, f 5 = 15 and f a = - 3 a . Substituting 15 for f 5 and - 3 a for f a in the equation f 5 - f a = - 15 yields 15 - - 3 a = - 15 . Subtracting 15 from both sides of this equation yields - - 3 a = - 30 . Dividing both sides of this equation by - 1 yields - 3 a = 30 . By the definition of absolute value, if - 3 a = 30 , then - 3 a = 30 or - 3 a = - 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.

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