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Composites Right to Left Simplify Use ( )!!

Inverses f -1 (x). Composites Right to Left Simplify Use ( )!!. Equations: 1)Replace f(x) with y 2) Change y and x 3)Solve for the new y 4) Write as f -1 (x) =. f(x) = 3x + 2 g(x)= x 2 + 1. Ex: f(x) = 3x + 2 y = 3x + 2 x = 3y + 2 x – 2 = 3y

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Composites Right to Left Simplify Use ( )!!

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  1. Inverses f-1(x) Composites Right to Left Simplify Use ( )!! Equations: 1)Replace f(x) with y 2) Change y and x 3)Solve for the new y 4) Write as f-1(x) = f(x) = 3x + 2g(x)= x2 + 1 Ex: f(x) = 3x + 2 y = 3x + 2 x = 3y + 2 x – 2 = 3y = y so f-1(x) = • g(-5) = (-5)2 + 1 = 26 • f (g(-5))  SUBSTITUTE -5 into g and • then substitute the answer into f • f((-5)2+1)f(26)=3(26)+1 79 • g o f(-5)  SUBSTITUTE -5 into f and then • substitute the answer into g • gof(-5)  g(f(-5))  g(3(-5) + 2)  g(-13)  • (-13)2 + 1  170 • f (g(x)) SUBSTITUTE ALL OF g(x) into f(x) • and simplify. USE ( ) around g(x) • f(g(x)) = f( x2 + 1)  3(x2 + 1)  3x2 + 3 Ordered Pairs: SWITCH x and y (3,4)  (4, 3) (2,-1)  (-1,2) Two functions are inverses if fog(x) = x and gof(x) = x Graphs: Reflection on y = x Intersection(s) at (x,x) The Solid and Dashed functions are inverses

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