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= x−4x_I The function f is defined by f(x). What 1 f(5)−f(a) = −15 value of a satisfies? −20
Correct answer: C (parsed from the explanation — this source omits an answer key for this item)
Explanation
= - Choice C is correct. It’s given that the function f is defined by f^xh x 4x . It’s 5 - =-15 also given that f^ h f^ah . Substituting 5 for x in the function = - 5 = 5-4 5 f^xh x 4x yields f^ h ^ h and substituting a for x in the function = - = - 5 =15 = - f^xh x 4x yields f^ah a 4a . Therefore, f^ h and f^ah 3a . 15 - 5 - =-15 Substituting for f^5h and 3a for f^ah in the equation f^ h f^ah 15- -3 =-15 15 yields a . Subtracting from both sides of this equation yields - -3 =-30 - -3 =30 a . Dividing both sides of this equation by 1 yields a . By -3 =30 -3 =30 -3 =-30 the definition of absolute value, if a , then a or a . - =-10 =10 Dividing both sides of each of these equations by 3 yields a or a , respectively. Thus, of the given choices, a value of a that satisfies 5 - =-15 10 f^ h f^ah is . 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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