f : R → R IS A FUNCTION SUCH THAT f ( x ) = 2 x + sin x ; THEN, F IS

f ′ ( x ) = 2 + cos x > 0 ; ∴ f is one-one f is continuous; lim x → ∞ f ( x ) ≡ ∞ ; lim x → − ∞ f ( x ) ≡ − ∞ ∴ f IS ONE-ONE AND ONTO

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Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMonotonicity-Increasing-DecreasingMedium2 minQB

MathematicsMediumsingle choice

$f : R \to R$ IS A FUNCTION SUCH THAT $f (x) = 2 x + sin x$ ; THEN, $F$ IS

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Answer:

Solution:

$f^{'} (x) = 2 + cos x > 0; ∴ f$ is one-one $f$ is continuous; $lim_{x \to \infty} f (x) \equiv \infty; lim_{x \to - \infty} f (x) \equiv - \infty$ $∴ f$ IS ONE-ONE AND ONTO

Stream:JEESubject:MathematicsTopic:Application of DerivativeSubtopic:Monotonicity-Increasing-Decreasing

⏱ 2mℹ️ Source: QB

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