Inverse Functions Flashcards
What’s an inverse function?
A function that reverses the operations of another function.
Let f(x) = x + 2, what function would reverse f’s changes? Let that function be g.
g(x) = x - 2.
Let f be a function, what notation is used to reffer to f’s inverse function?
f^-1(x).
What’s the relationship of the domain and range of f and f^-1?
f’s domain is f^-1’s range and vice versa.
Let f and f^-1 be functions. Explain why f’s domain is f^-1’s range and vice versa.
The inverse function takes the output of 𝑓 as input, and reverses it back to its original value, this value is the output, thus the range-domain relationship.
Let f(x) = x/2, how would f’s inverse function look like?
f^-1(x) = x*2 .
How is the inverse of a function found?
By replacing f(x) with y, and solving for x. Finally, replace x with f^-1(x) and y with x.
Using a step-by-step method, explain how the inverse of the function f(x) = 2 + x can be found.
- f(x) = 2 + x is transformed into x = 2 + y
- y = x - 2
- f^-1(x) = x - 2
How is the strategy for finding the inverse of a function called?
Switch-and-solve.
What is the horizontal line test?
A method of testing if a function has an inverse function. If the graph of a function is intercepted with a horizontal line more than once, then this function doesn’t have an inverse function.
Using the horizontal line test, test if f(x) = x^2 has an inverse function.
It doesn’t, a horizontal line can be drawn that intercepts the graph more than once.
What is a one-to-one function?
A function in which no two different ordered pairs have the same second component.
What kind of functions can only have inverse functions?
One-to-one functions.
Is f(x) = x^2 a one-to-one function?
No.
What is the connection between the graphs of f and f^-1?
The graphs are symmetrical with respected to the line y = x.
