Inverse Functions Inverse Functions

For example, let’s take a look at the square function: f(x) = x2 The inverse of a given function will “undo” what the original function did. For example, let’s take a look at the square function: f(x) = x2 x f(x) y f--1(x) 9 3 3 9 9 3 3 9 9 3 3 9 9 3 3 x2 9 9 3 3 9 9 9 3 3 3 9 9

For example, let’s take a look at the square function: f(x) = x2 In the same way, the inverse of a given function will “undo” what the original function did. For example, let’s take a look at the square function: f(x) = x2 x y f--1(x) f(x) 5 25 5 5 5 25 25 5 5 25 25 5 5 x2 25 5 5 25 5 25 25 5 25 5 5 5

For example, let’s take a look at the square function: f(x) = x2 In the same way, the inverse of a given function will “undo” what the original function did. For example, let’s take a look at the square function: f(x) = x2 x f(x) y f--1(x) 11 121 11 11 11 121 121 11 11 121 121 11 11 x2 121 121 121 11 11 121 121 11 11 121 121 121 11 121 11

Graphically, the x and y values of a point are switched. The point (4, 7) has an inverse point of (7, 4) AND The point (-5, 3) has an inverse point of (3, -5)

Graphically, the x and y values of a point are switched. If the function y = g(x) contains the points x 1 2 3 4 y 8 16 then its inverse, y = g-1(x), contains the points x 1 2 4 8 16 y 3 Where is there a line of reflection?

The graph of a function f(x)=2x and its inverse are mirror images about the line y = f(x) y = x y = f-1(x) y = x

Find the inverse of a function : f(x) = 6x- 12 y = 6x - 12 Step 1: Switch x and y: x = 6y - 12 Step 2: Solve for y:

Example 2: f(x) = 3x2 + 2, D: x>=0; R: y>=2 Given the function : y = 3x2 + 2 find the inverse: Step 1: Switch x and y: x = 3y2 + 2 Step 2: Solve for y: