# To algebraically find the equation of 1 f ³

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To algebraically find the equation of 1 f ³ , interchange x and y in the equation of f, then resolve for y. Example 6 If ( ) 4 2 f x x ³ , determine if ( ) f x is one-to-one. If it is, sketch the graph of f, then graphically and algebraically find 1 f ³ . Find (2) f and 1 (6) f ³ . If ( ) f x is a one-to-one function over a domain, then it is an invertible, meaning, it has an inverse function, ( ) g x , such that 1 ( ) ( ) g x f x ³ . y 4x 2 m 4 f x _4 2 iii a z f x _4 x 1 4y 2 2 4 y f 67 446 2 4 12 _y f Lx 4 I 3 2 4 2 2 6 2

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Example 7 Let ( ) g x be the inverse of 3 ( ) 2 1 5 f x x ³ ³ ³ . Find a) g b) g f and c) f g . Theorem of Inverses What does this say in student terms? Example 8 Let ( ) h x be in the inverse of 2 1 ( ) 4 3 x g x x ³ ´ . Find h, then verify, using the theorem above, to verify you have found the correct inverse. Give the domain of both h and g . Two functions f and g are inverses IFF ± ² ± ² ( ) ( ) f g x x g f x f x g Cx a y 2 VE s x 27 5 5 2 f Ix E 3 y l f Ex E g C Ex E t l g x a h x g l x y 2 14 1 3 4yt3 X 2 C4yt3 4yt3 x 4 gt3 2g I 4xyt3x 2g I 4xy 2g I 3x y 4 21 1 3 g had g x
• Fall '19
• Inverse function, Injective function

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