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

If f(x) = x3 + 3x2 + 12x − 2sinx, where f: R → R, then 

(A)  f(x) is many-to-one and onto 

(B)  f(x) is one-to-one and onto 

(C)  f(x) is one-to-one and into 

(D)  f(x) is many-to-one and into 

1 Answer

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by (53.3k points)
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Best answer

Correct option  (B) f(x) is one-to-one and onto

Explanation :

We have f(x) = x3 + 3x2 +12x -12x - 2sinx 

 Therefore, f′(x) = 3x2 + 6x +12 - 2cosx

Hence, f ′(x) > 0 ∀x. Therefore, f(x) is an increasing function and thus f(x) is one-to-one and onto.

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