Foldie-do for Inverses Fold your paper over (top to bottom leaving about an inch at the bottom). f  1 (x) © 2010, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgiaadapted from various sources

Find the inverse relation. x y Switch the coordinates of each ordered pair.

Practice 1 Find the inverse of each relation. State whether the relation is a function. State whether the inverse is a function. a) {(1,2), (4,-2), (3,2)} inverse: {(2,1), (-2,4), (2,3)} function not a function b) {(-2,4), (3,-4), (-8,-5)} inverse: {(4,-2), (-4,3), (-5,-8)} function

Find an inverse of y = -3 x Switch x & y. 2. Solve for y. x = -3y+6-6 x - 6 = -3y -3 -3

Practice x - 3 = 2y 22 Find the inverse of

1. Switch x & y. 2. Solve for y. B. Take the square root of both sides Practice 3 A. Add 3 to both sides

Activity 1)Graph y = 2x – 1. 2) Graph y = x. 3) Graph the inverse of y = 2x – 1.

You try!! 4) Graph y = -2x + 5 5) Graph y = x. 6) Graph the inverse of y = -2x + 5.

Graph to verify the inverse. The graph of f -1 (x) is obtained by reflecting the graph of f(x) across the line y = x. f(x) = 3x  2 f  1 (x) =.

Solution 22220 5555 1111 f(x) = 3x  2 x 2222 1111 5555x f  1 (x) =

Determine if f(x) and g(x) are inverses of each other. 1.f(x) = 3x + 9 and g(x) = (1/3)x – 3 2.f(x) = 6x - 5 and g(x) = (1/6)x – 5 3.f(x) = -3x + 5 and g(x) = (-1/3)x + (5/3) Practice 4

f(f -1 (x)) = x f -1 (f(x)) = x Given that f(x) = 7x  2, use composition of functions to show that g(x) = (x + 2)/7 is the inverse of f(x).

Solution

Practice 5 Show that f(x) = 4x – 3 and are inverses of each other.