I am having trouble with another math problem concerning inverses. My book says the following:

"

Basic Rule for Finding InversesTo find the inverse of a functionf, we solve the equation

(f·f<sup>-1</sup>)(t) =t

for the functionf<sup>-1</sup>(t)

EXAMPLE 1.40

Find the inverse of the functionf(s) = 3s.

SOLUTION

We solve the equation

(f·f<sup>-1</sup>)(t) =t

This is the same as

f(f<sup>-1</sup>(t)) =t

We can rewrite the last line as

3 ·f<sup>-1</sup>(t) =t

or

f<sup>-1</sup>)(t) =t/3

"

Where I am confused is where the equation replaces (f(f<sup>-1</sup>)(t)) for 3 ·f<sup>-1</sup>(t).

I think I may have a very weak grasp of how it might work, but not any kind of solid rule to go by. This is what I've come up with: The value of a function for any given variable should be divisable by both the variable and a scaler that is not necesarily the same number for every variable value... What good is that knowledge though if the scaler is not always the same number? Perhaps the writer just recognized a pattern with this specific problem and used it to quickly solve the problem.