How can you compose functions and find inverse functions?

Answer 1

Compose functions: First you apply one function to the original input, then you apply a second function to the result.

Inverse function: I'll give an example. Assume your function is f(x) = 3x + 1. You can write the function as:

y = 3x + 1

... and solve for "x". Finally, exchange "x" and "y". In this case, solving for "x", you get:

y = 3x + 1

3x + 1 = y

3x = y - 1

x = (y - 1)/3

If you exchange "x" and "y", you get:

y = (x - 1)/3

Or, using functional notation, and using the function name "g" for the inverse of "f":

g(x) = (x-1)/3

Obviously, actually solving for the "other variable" is not always easy, and sometimes you won't be able to write the inverse function in an explicit way.