NTA Abhyas JEE Main2020MathematicsFunctionsPractice

If f x = 2 x − sin x , f : R → R and g x = x 1 3 , g : R → R , then

Options

Aboth f and g are onto
Bgof is one-one
Cboth f and g are one - one
DAll are true

Correct answer

D. All are true

Step-by-step solution

f ' x = 2 - cos x ∀ x ∈ R⇒ one - one, and g ' x = 1 3 x - 2 / 3 > 0 ⇒ one - one Since, both g and f are one - one, hence, gof is also one - one. Range of f x is - ∞ , ∞ as f x is continuous and f x → ± ∞ as x → ± ∞ . Also, since domain of g x is R , y = x 1 3 ⇒ x = y 3 ⇒ y 3 ∈ - ∞ , ∞ ⇒ y ∈ - ∞ , ∞ ⇒ Range of g x is also R .

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