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$The function f : (- \infty, - 1) \to (0, e^{5}] defined by f (x) = e^{x^{3} - 3 x + 2} is$

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a

many-one and onto

b

many-one and into

c

one-one and onto

d

one-one and into

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detailed solution

Correct option is D

fx =ex3-3x+2 ⇒f'x=ex3-3x+2 ·3x2-3 >0 for all x∈-∞,-1 therefore f is increasing function and hence it is one-one Range of fx =0, e4 since x tends to -∞ ⇒fx tends to 0 and x→-1 ⇒fx→e4 Range of f ≠Codomain of f ⇒ it is not onto i.e into

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Similar Questions

Which of the following statements are incorrect?

$I. If f (x) and g (x) are one-one then f (x) + g (x) is also one-one$

$II. If f (x) and g (x) are one-one then f (x) \cdot g (x) is also one-one$

$III. If f (x) is odd then it is necessarily one-one.$

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