Question

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Answer 1

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Answer 2

To prove a function is bijective, you need to prove that it is injective and also surjective. "Injective" means no two elements in the domain of the function gets mapped to the same image. "Surjective" means that any element in the range of the function is hit by the function. Let us first prove that is injective..

injective,,,,

f(x)=x^3+x

let x1 and x2 belongs to R

such that x1 is not equal to x2

f(x1)=x1^3+x1

f(x2)=x2^3+x2

it clearly shows that f(x1) is not equal to f(x2)

so it is injective

for surjective

let f(x)=x^3+x,,,,,,,(1)

y=x^3+x

find x and substitute in (1)

at last

f(x)=y

so surjective proved

bijective