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in Sets, relations and functions by (53.3k points)

If f(x)  + 2f (1/x) = 3x,x ≠ 0 and S = {x ∈ R: f(x) = f(-x)}, then S

(A)  contains more than two elements.

(B)  is an empty set.

(C)  contains exactly one element.

(D)  contains exactly two elements

1 Answer

+1 vote
by (53.1k points)
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Best answer

Correct option (D) contains exactly two elements.

Explanation :

We have

f(x) + 2f(1/x) = 3x,x ≠ 0

Replacing x by 1/2, we get

Therefore, S contains only two elements.

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