Functions can be operated on following the order of operations just like numbers and variables

sum          (f+g)(x) = f(x) + g(x)
difference   (f-g)(x) = f(x) - g(x)
product      (f*g)(x) = f(x) * g(x)
quotient     (f/g)(x) = f(x) / g(x)
composite    (f°g)(x) = f(g(x))

Inverse functions

If you have a "one to one" function (a function that always has one output for one input) you can find that functions inverse (the function that undoes it)

x = f^-1(f(x))

Find the inverse of f(x) = 2/3x - 4 by swapping the variable and solving for y

x = 2/3y - 4
...
y = 3/2x + 6