Inverses By Jeffrey Bivin Lake Zurich High School

Inverses By: Jeffrey Bivin Lake Zurich High School jeff. bivin@lz 95. org Last Updated: November 17, 2005

Definition Inverse Relation A relation obtained by switching the coordinates of each ordered pair. Jeff Bivin -- LZHS

INVERSE RELATIONS Jeff Bivin -- LZHS

Relation { (1, 4), (4, 6), (-3, 2), (-4, -2), (-1, 5), (0, 1) } Inverse { (4, 1), (6, 4), (2, -3), (-2, -4), (5, -1), (1, 0) } Jeff Bivin -- LZHS

Relation {(-4, -6), (1, 4), (2, 6), (-1, 0), (-4, 3), (4, -2)} Inverse {(-6, -4), (4, 1), (6, 2), (0, -1), (3, -4), (-2, 4)} Jeff Bivin -- LZHS

f(x)= x 2 Jeff Bivin -- LZHS

f(x)= x 2 Jeff Bivin -- LZHS

G(x) Jeff Bivin -- LZHS

G(x) Jeff Bivin -- LZHS

G(x) Jeff Bivin -- LZHS

G(x) Jeff Bivin -- LZHS

f(x)= x 3 Jeff Bivin -- LZHS

Find the inverse Jeff Bivin -- LZHS

Find the inverse Jeff Bivin -- LZHS

Find the inverse Jeff Bivin -- LZHS

Inverse functions Two functions, f(x) and g(x), are inverses of each other if and only if: f(g(x)) = x and g(f(x)) = x Jeff Bivin -- LZHS

Are these functions inverses? Jeff Bivin -- LZHS

Are these functions inverses? Jeff Bivin -- LZHS

One-to-One functions • A function is one-to-one if no two elements in the domain of the function correspond to the same element in the range. Domain Range 2 1 5 9 Jeff Bivin -- LZHS F(x) -5 4 One-to-One

f(x)= x 2 Jeff Bivin -- LZHS