Inverse Functions

Front

What is true about a function if its inverse is also a function?

Back

It is one-to-one.

Front

How is the inverse of the function f(x) written?

Back

f^{-1}(x)

Front

What must be true for two functions to be inverses?

Back

f(g(x)) = g(f(x)) = x.

Front

If the equation of f(x) goes through (1, 4) and (4, 6), what points does f^{-1}(x) go through?

Back

(4, 1) and (6, 4).

Front

What does it mean to find the inverse of a function?

Back

The x's and y's are switched.

Front

What is a one-to-one function?

Back

A function where each output is produced by exactly one input.

Front

What is the diagonal line test?

Back

A method to determine if a function is one-to-one by checking if any horizontal line intersects the graph more than once.

Front

What is the relationship between a function and its inverse?

Back

The inverse function reverses the effect of the original function.

Front

If f(x) = 2x + 3, what is f^{-1}(x)?

Back

f^{-1}(x) = (x - 3)/2.

Front

What is the domain of a function's inverse?

Back

The range of the original function.