Original
If {{MATH_101}} converts Celsius measurements to Fahrenheit measurements of
temperature, then {{MATH_102}} converts Fahrenheit measurements to
Celsius measurements of temperature.
To find the inverse function, first note that
{{MATH_103}}
Now write out the left-hand side of the equation
{{MATH_104}}
and solve for {{MATH_105}}.
{{ENV_106}}
So {{MATH_107}} is the inverse
function of {{MATH_108}}, which converts a Fahrenheit measurement back into
a Celsius measurement.
Finally, we could check our work again using the definition of inverse functions.
We have already guaranteed that
{{MATH_109}}
since we solved for {{MATH_110}} in our calculation. On the other hand,
{{ENV_111}}
which shows that {{MATH_112}}.
{{CMD_113}}
{{CMD_114}}