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Inverse Functions and Relations

By Hamda Salah

Finding An Inverse Relation

- KEY CONCEPT Two relations are inverse relations

if and only if whenever one relation contains the

element (a,b) the other contains the element

(b,a). - EXAMPLE Q (1,2) (4,9) (3,5)
- S (2,1) (9,4) (5,3)
- Q and S are inverse relations
- This is prevalent in geometry when trying to

find the reflection of a specific shape on a

grid.

Find Inverse Function

Follow along on page 391 example 2. Example

will be worked out KEY CONCEPT Suppose f and f

1 are inverse functions. Then, f(a) b if and

only if f 1 (b) a. Step 1 Replace f(x) with y

in the original problem Step 2 Interchange x

and y Step 3 Solve for y Step 4 Replace y with

f 1 (x).

Verifying Two Functions Are Inverses

Determine whether f(x) 5x10 and g(x) 1/5x

2 are inverse functions (f o g) f(g(x) ) (g o

f)(x) g(f(x) ) f( 1/5x 2) g (5x

10) 5( 1/5x 2) 10

1/5 (5x 10) - 2 x 10 10 x 2

2 x x The functions are

inverses since both (f o g) (x) and (g o f) (x)

equal x.

DONE

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