NTA Abhyas JEE Main2020MathematicsFunctionsPractice

Consider a function f : R → R defined by f x = x 3 + 4 x + 5 , then

Options

Af is one-one but not onto
Bf is onto but not one-one
Cf is one-one and onto
Df is neither one-one nor onto

Correct answer

C. f is one-one and onto

Step-by-step solution

Given, f x = x 3 + 4 x + 5 Now, f ′ x = 3 x 2 + 4 > 0 , ∀ x ∈ R ∴ f x is strictly increasing function ∴ It is one-one Clearly, f x is a continuous function and also increasing on R lim x → - ∞ f x = - ∞ and lim x → ∞ f x = ∞ ∴ f x takes every value between - ∞ and ∞ . Thus, f x is an onto function.

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