Prove that $f(x)=x(1-x)$ on $I$ is conjugate to $g(x)=x^2-\frac{3}{4}$ on a certain interval in $\mathbb{R}$. Determine this interval.
Suppose $I$ and $J$ are intervals and function $f$ from $I$ to $I$ and $g$ from $J$ to $J$ we say that $f$ and $g$ are conjugate if there is a homeomorphism $h$ from $I$ to $J$ such that $h$ satisfies the conjugacy equation $h\circ f = g\circ h$.