Hi, How do I prove that this functions is injective? a.) f : x --> x³ + x x ∈ R
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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 $\displaystyle x=y$.
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
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