, a is a real number.

What I did:

Let 0, 1)\mapsto \mathbb{R}, f(x)=\frac{\sqrt{1+2x}+4\sqrt{1-x}}{\sqrt{(1+2x)(1-x)}}\Rightarrow \displaystyle f(1-a)=f(a)" alt="\displaystyle f0, 1)\mapsto \mathbb{R}, f(x)=\frac{\sqrt{1+2x}+4\sqrt{1-x}}{\sqrt{(1+2x)(1-x)}}\Rightarrow \displaystyle f(1-a)=f(a)" />. I want to prove that f is injective/ strictly monotone.

Well, that is my idea, but anything else would be okay. Thanks in advance.