Section 33 Inverse Functions and Relations

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Section 3-3 Inverse Functions and Relations

• This is going to be fun.
• Well, maybe

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Example
Axis of Symmetry? y x
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Inverse Relations

• Relations are inverses iff. One relation contains
  (a,b) and the other contains (b,a).
• f -1 (x) is a reflection of f(x) over the y x
  line.

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Find The Inverse
v3 v4-x yv3 v3 v3 v4-x y
3 v12-3x y 3 and finally f -1 (x)
1/3 v12-3x

• f(x) 4-3x2
• y 4-3x2
• x 4-3y2
• x-4 -3y2
• x-4 y2-3
• 4-x y2 3
• v4-x y v3

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Vertical and Horizontal Line Tests

• To test whether a graph is a function use the
  vertical line test.
• To test whether f -1 (x) will be a function use a
  horizontal line test.
• Check out the function f(x) 4-3x2
• Is it a function? Yes
• Will its inverse be a function?

No!
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Polynomial Functions xn

• If n is even ? the inverse is not a function.
• If n is odd ? the inverse is a function.

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GRAPH!!!

• y 3(vx-1) 2
• Not a Function!!

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Homework

• Page 130 14-26 even, 27, 31, 33, 35-37
• Tanvirkamal Made It!!!