suppose that $\displaystyle f:[0,1]-->[0,1]$ is continuous. By considering the function $\displaystyle g(x)=(f(x))^2-x$, or otherwise, prove that there must be a point $\displaystyle c\in[0,1]$ with $\displaystyle f(c)=\sqrt{c}$.

I have no idea so can you help please?

Thanks