Suppose I have an odd, increasing function $h$ with $h(0)=0$ and an unknown increasing function $f(D)$, $f(0)=0$.
$$\phi(h(f(D)) h(f(D)) h'(f(D)) f'(D)=D$$
where $\phi$ is the standard normal pdf
From the above equation, we can see that $D$ spans the real line and the when the RHS is $> 0$ so is the LHS and vice versa.
But, I can rewrite the above equation as:
$$\implies 0.5 D^2=-\phi(h(f(D)) $$
which does not make sense since the LHS is $> 0$ and the RHS is $< 0$