Hi, this exercise is giving headaches . I only need help with Part A because I know part B and have an idea of how to solve other exercises similar to part C. Thanks a lot!

The whole exercise says:

"Let $\displaystyle f(x)=(x^2+3)/(2x)$ for $\displaystyle x \neq 0$. Define a sequence of real numbers $\displaystyle x_n$ by

$\displaystyle x_{n+1}=f(x_n)$ for $\displaystyle n \ge 1$, $\displaystyle x_1=2$.

A) Show that if $\displaystyle x>\sqrt{3}$, then $\displaystyle f(x)>\sqrt{3}$.

B) Show that if $\displaystyle x>\sqrt{3}$, then $\displaystyle x>f(x)$.

C) Conclude that the sequence $\displaystyle x_n$ converges."