Proving that a function is bijective I have trouble figuring out this problem:
Prove that the function $f: [0,\infty)\rightarrow[0,\infty)$ defined by $f(x)=\frac{x^2}{2x+1}$ is a bijection. 
Work: First, I tried to show that $f$ is injective. $\frac{a^2}{2a+1}=\frac{b^2}{2b+1}$
I got $a^2(2b+1)=b^2(2a+1)$. However, I get stuck here and cannot simplify the equation to get $a=b$, which would prove that the function is injective. 

One way to prove injectiveness in this case, is to prove that the function is strictly increasing. This can be done via derivative.
