What happens when we compose f and g ?
Notice that one function ‘undoes’ the other, producing a
final answer of x in both cases.
We say that f and g are inverses of each other.
• Definition : Two functions f and g are inverses of each other if
• example : Verify that and are inverses of each other.
• Notation : The inverse of function f is denoted by
• In the example above, we could write and
• We can also restate the definition of inverse functions as
• example : Verify that if , then
• How do we find the inverse of a function?
• example : Find the inverse of y = 3x + 2
1. y = 3x + 2
2. x = 3y + 2 ( interchange x and y )
3. ( solve for )
• example : Find the inverse of f (x) = 4 − 2x
• Does every function have an inverse function?
• Horizontal Line Test : A function has an inverse if no
horizontal straight line intersects its graph
more than once. The function is said to be one-to-one.
• example : Does y = x2 have an inverse?
• example : Does y = x2 , x ≥ 0 have an inverse?