Suppose that f is continuous on [0, 6] and that the only solutions of the equation f (x) = 3 are x = 1 and x = 5. If f (4) = 2, then which of the following statements must be true? (i) f (2) 3 (iii) f (6)

Question

Suppose that  f  is continuous on [0, 6] and that the only solutions of the equation  f (x) = 3 are x = 1 and x = 5. If  f (4) = 2, then which of the following statements must be true?

(i)  f (2)  <  3
(ii)  f (0)  >  3
(iii)  f (6)  <  3

(A) all of them    (B) (ii) and (iii)    (C) (i) and (iii)    (D) (ii) only    (E) (i) only    (F) (iii) only    (G) (i) and (ii)    (H) none of them

dumbcow · Answer

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from diagram you see that f(0) and f(6) could be anything but f(2) is definitely less than 3