Final answer:
A composition of functions is the process of applying one function to the output of another function, while an inverse function undoes the effect of another function.
Step-by-step explanation:
A composition of functions is the process of applying one function to the output of another function. More specifically, if we have two functions, f(x) and g(x), then the composition of these functions is denoted as (f ∘ g)(x) and is defined as f(g(x)). The composition of two functions combines their individual operations.
An inverse function is a function that undoes the effect of another function. If we have a function f(x), its inverse function is denoted as f^(-1)(x) and is defined as the function that, when applied to the output of f(x), gives back the original input x.
To find the inverse of a function, we typically follow these steps:
- Replace the function notation f(x) with y.
- Swap the x and y variables.
- Solve the resulting equation for y to express it in terms of x.
- Replace y with f^(-1)(x) to represent the inverse function.