Is f(s)=x^3 a bijection from RR to RR?

alesterp

alesterp

Answered question

2021-09-13

Is f(s)=x3 a bijection from R to R?

Answer & Explanation

Bertha Stark

Bertha Stark

Skilled2021-09-14Added 96 answers

f:AB is one-to-one if a,bA,f(a)=f(b)a=b
Assume that x,yR,f(x)=f(y).
f(x)=f(y)
x3=y3
x=y
Thus,
f(x)=x3 is one-to-one
"For the function to be onto:
f(x)=y
let yR
Choose x to be y13.
Then,
xR
and
f(x)=x3
=(y13)3
=y
Thus f(x)=x3 is onto
Since its

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