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in Sets, relations and functions by (53.1k points)

Let f (x) = x2 - 4/x2 + 4 for |x|>2. Then the function f :(-∞, - 2)∪(2,∞) →(-1,1) is 

(A)  One-to-one and into

(B)  One-to-one and onto

(C)  Many-to-one and into

(D)  Many-to-one and onto 

1 Answer

+1 vote
by (53.3k points)
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Best answer

Correct option (C) Many-to-one and into

Explanation :

Let us consider

Lf'(2) ≠ Rf'(2)

Therefore, f(x) is many-to-one. Now, for each y∈(-1, 1), there does not exist x ∈ X  such that f(x) = y. Hence, f is into.

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