# Combining two equations for two conditions

I am trying to construct a peak model equation where:

When x is equal to or less than the mean y is calculated using the Gaussian distribution equation, and when x is more than the mean the Lorentzian/Cauchy model is used instead.

I wanted to know if there was a specific mathematical way of writing this, or the best way to represent this (in equation form) in scientific text. I am not a mathematician, so apologies if this is a very simple question.

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Sounds like a piecewise defined function. If $M$ is the mean, you can write it $$y = \left\{\begin{array}{ll} \text{<formula 1>} &\text{if }x\leq M,\\ \text{<formula 2>} &\text{if }x\gt M. \end{array}\right.$$