^{24}This inversion of function caused by the swapping of input and feedback components in an operational amplifier
circuit points to a fundamental principle of negative feedback networks: namely, that placing a mathematical element within
the feedback loop causes the amplifier to exhibit the inverse of that element’s intrinsic function. This is why
voltage dividers placed within the feedback loop cause an opamp to have a multiplicative gain (division →
multiplication). A circuit element exhibiting a logarithmic response, when placed within a negative feedback loop, will
cause the amplifier to exhibit an exponential response (logarithm → exponent). Here, an element having a
time-differentiating response, when placed inside the feedback loop, causes the amplifier to time-integrate (differentiation
→ integration). Since the opamp’s output voltage must assume any value possible to maintain (nearly) zero
differential voltage at the input terminals, placing a mathematical function in the feedback loop forces the output
to assume the inverse of that function in order to “cancel out” its effects and achieve balance at the input
terminals.