每日一题

Mathematics>Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer.

If the function function f is defined by function f of x = (x-a)(x-b)/(x-c), where 0 less than a less than b less than c, for which of the following values of x is function f undefined?

I. a
II. b
III. c

(A) None
(B) I only
(C) III only
(D) I and II only
(E) I, II, and III

答案和解析

答案：C

解析：

If x = a, then (x-a)(x-b)/(x-c) = (a-a)(a-b)/(a-c) = 0/(a-c) = 0. If x = b, then (x-a)(x-b)/(x-c) = (b-a)(b-b)/(b-c) = 0/(b-c) = 0. If x = c, then (x-a)(x-b)/(x-c) = (c-a)(c-b)/(c-c) = (c-a)(c-b)/0, which is not defined because division by 0 is undefined. Therefore, of the three values, a, b, and c, the only one for which function f is undefined is c. Thus the correct response is III only.