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Higher Order Derivatives

40. Consider ...

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40. Consider f: R → R & f(x) = x3 + x2 + ax + 4 be bijective, then interval for a is?

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Q. Assertion :Let

f : R \to R

f (x) = x^{3} + x^{2} + 100 x + 5 sin x

f (x)

is bijective. Reason:

3 x^{2} + 2 x + 95 > 0 x \in R

.

f (x) = x^{3} + 3 x^{2} + 12 x - 2 sin x

f : R \to R

, then prove that

f

f : R \to R

^{'} k^{'}

be largest natural number for which

f (x) = x^{3} + 2 k x^{2} + (k^{2} + 12) x - 12

is a bijective function, then

\frac{f (1) + f^{- 1} (49)}{10}

Q. A function f : R → R is defined as f(x) = x³ + 4. Is it a bijection or not? In case it is a bijection, find f⁻¹ (3).

\to

R be function defined by f(x) =

x^{3}

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