- #1

pondzo

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## Homework Statement

$$f:\mathbb{R}\rightarrow\mathbb{R}~~\text{where}~~f(x)=x^3+2x^2-x+1$$

Show if f is injective, surjective or bijective.

## Homework Equations

## The Attempt at a Solution

f is obviously not injective (and thus not bijective), one counter example is x=-1 and x=1.

I can see from the graph of the function that f is surjective since each element of its range is covered.

But I am not sure how i can formally write it down. If i try this;

##\text{let}~y\in\mathbb{R}## and then try to find which ##x\in\mathbb{R}## maps to y then the algebra is going to get really messy and it would take a long while. Is there a faster and easier way of showing f is injective? Can i draw the function and show that all of the co-domain is covered, or is this not formal enough?

Thank you for your time.