f x = 59 - 2 x The function f is defined by the given equation. For which of the

Question

f x = 59 - 2 x The function f is defined by the given equation. For which of the following values of k does f k = 3 k ?

Accepted Answer

Choice A is correct. The value of k for which f k = 3 k can be found by substituting k for x and 3 k for f x in the given equation, f x = 59 - 2 x , which yields 3 k = 59 - 2 k . For this equation to be true, either - 3 k = 59 - 2 k or 3 k = 59 - 2 k . Adding 2 k to both sides of the equation - 3 k = 59 - 2 k yields - k = 59 . Dividing both sides of this equation by - 1 yields k = - 59 . To check whether - 59 is the value of k , substituting - 59 for k in the equation 3 k = 59 - 2 k yields 3 - 59 = 59 - 2 - 59 , which is equivalent to - 177 = 177 , or - 177 = 177 , which isn't a true statement. Therefore, - 59 isn't the value of k . Adding 2 k to both sides of the equation 3 k = 59 - 2 k yields 5 k = 59 . Dividing both sides of this equation by 5 yields k = 59 5 . To check whether 59 5 is the value of k , substituting 59 5 for k in the equation 3 k = 59 - 2 k yields 3 59 5 = 59 - 2 59 5 , which is equivalent to 177 5 = 177 5 , or 177 5 = 177 5 , which is a true statement. Therefore, the value of k for which f k = 3 k is 59 5 . Choice B 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.

Question f-x-59