Today in Pre-Calculus Go over homework questions Notes: Inverse functions Homework

Inverse Functions Reversing the x- and y-coordinates of all the ordered pairs in a relation gives the inverse. The inverse of a relation is a function if it passes the horizontal line test. A graph that passes both the horizontal and vertical line tests is a one-to-one function. This is because every x is paired with a unique y and every y is paired with a unique x.

Inverse Functions Definition: If f is a one-to-one function with domain D and range R, then the inverse function of f, denoted f –1, is the function with domain R and range D defined by f –1 (b)=a iff f(a)=b

Graphing Inverses

Example a)f(x) = 2x – 3 y = 2x – 3 x : (-∞,∞), y: (-∞,∞) x = 2y – 3 y : (-∞,∞), x: (-∞,∞) x + 3 = 2y D: (-∞,∞)

Example f(x) = y = x = [0,∞), y = [0,∞) x = y = [0,∞), x = [0,∞) y = x 2 f –1 (x) = x 2 D=[0,∞)

Example x ≠ -2, y ≠ 1 y ≠-2, x ≠1 x(y+2) = y xy + 2x = y 2x = y – xy 2x = y(1-x)

Inverse Composition Rule states that a function f is one-to-one with inverse function g iff f(g(x)) = x for every x in the domain of g and g(f(x)) = x for every x in the domain of f. Used to verify that f and g are inverses of each other.

Example

Homework pg 135: 13 – 31 odd Quiz: Tuesday, October 8 Chapter 1 test: Friday, October 11