- #1

soopo

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## Homework Statement

Prove that the derivate of [tex]y = \frac {1} {2} ax^{2} + bx[/tex] is a bijection, when [tex] a, b, x \in \Re [/tex]

## The Attempt at a Solution

y' = 2ax + b is a linear mapping, where [tex] a, b, x \in \Re [/tex].

The mapping is [tex]\Re \rightarrow \Re [/tex].

The mapping is an injection as each element in the domain maps to codomain.

The mappning is a surjection as elements in the domain maps all elements in the

codomain.

(I am not sure about the proofs for the injection and surjection)

Thus, the derivate is bijection, since it is an injection and surjection.