Kenneth Rosen Edition 6th Exercise 2.3 Question 18 (Page No. 147)

Question

Consider all below functions are from $R \rightarrow R$

Determine whether these functions are one-to-one, and onto.

(a)$f(x)=-3x+4$ -->Bijection

(b)$f(x)=-3x^2+7$-->Not one-to-one and not onto

(c)$f(x)=\frac{x+1}{x+2}$--->one-to-one but not onto

(d)$f(x)=x^5+1$--->Bijection

Are my answers correct.?

Comments

Any reference for your statement?

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Since Odd Power Function is Strictly Increasing, is injective. From Existence of Positive Root of Positive Real Number we have that: ∀ x ∈ R ≥ 0 : ∃ y ∈ R : y n = x. ... So when is odd, is both injective and surjective, and so by definition bijective.

copied from https://proofwiki.org/wiki/Integral_Power_Function_is_Bijective_iff_Index_is_Odd

i think they want to say odd power function is bijective over real no

 Ayush Upadhyaya tell me is it right ?

 

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@srestha-Yes $x^5+1$ is a bijective function.

https://math.stackexchange.com/questions/2990967/is-the-below-function-surjective?noredirect=1#comment6171642_2990967