1. ## Injective function

Hi,

How do I prove that this functions is injective?

a.) f : x --> x³ + x x ∈ R

2. Originally Posted by Hellbent
Hi,

How do I prove that this functions is injective?

a.) f : x --> x³ + x x ∈ R
Assume $\displaystyle f(x) = f(y)$ for some $\displaystyle x,y \in \mathbb{R}$

Then, $\displaystyle x+x^3 = y+y^3$. You need to finish the proof by showing that $\displaystyle x=y$.

3. Originally Posted by Defunkt
Assume $\displaystyle f(x) = f(y)$ for some $\displaystyle x,y \in \mathbb{R}$

Then, $\displaystyle x+x^3 = y+y^3$. You need to finish the proof by showing that $\displaystyle x=y$.
That's the problem I have.

f(a) = a³ + a, f(b) = b³ + b
f(a) = f(b) => a³ + a = b³ + b => a³ = b³
=> a = b
therefore f is one-to-one