Inverse of a Function Defined by Ordered Pairs: If f ( x ) is a one-to-one function whose ordered pairs are of the form ( x , y ) , then its inverse function f -1 ( x ) is the set of ordered pairs ( y , x ) Horizontal Line Test: If every horizontal line, intersects the graph of a function in at most one point, it is a one-to-one function

Inverse Functions: For every x in the domain of one-to-one function f and f -1 , f -1 ( f ( x ) = x f ( f -1 ( x ) = x f -1 ( f ( x ) = x f ( f -1 ( x ) = x How to Find the Inverse of a One-to-One Function: Step 1.

logarithmic function — The function f ( x ) = log a x is the logarithmic function with base a , where a > 0 , x > 0 , and a ≠ 1 . y = log a x is equivalent to x = a y. one-to-one function — A function is one-to-one if each value in the range has exactly one element in the domain. For each ordered pair in the function, each y -value is matched with only one x -value. exponential function — An exponential function, where a > 0 and a ≠ 1 , is a function of the form f ( x ) = a x. asymptote — A line which a graph of a function approaches closely but never touches.