The...er...derivendicular

Calculus Level pending

In this problem, two functions are defined to be perpendicular at all x in their domain if for every x in their domain, the tangent lines of those functions at x are perpendicular.

A function \( f(x) \) defined on \( x \leq 0 \), is perpendicular at all x in their domain to the function \( f'(x) \).

If \(f(0) = 0\), what is \(f(-4.5)\))?

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