inverse relations and functions

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Inverse Functions and Relations
By Hamda Salah
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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.

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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).
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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.
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DONE