How to FIND an Inverse How to VERIFY an Inverse x f(x)f(x)f(x)f(x) 0 2 3 xf  1 (x) 5 -2 4 7 f(x) = 3x  2 f () = 3( )  2 f (f  1 (x)) = 3( )  2 x +

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How to FIND an Inverse How to VERIFY an Inverse x f(x)f(x)f(x)f(x) xf  1 (x) f(x) = 3x  2 f () = 3( )  2 f (f  1 (x)) = 3( )  2 x © 2010, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia(MCC9-12.F.BF.4; MCC9-12.F.BF.4a; MCC9-12.F.BF.4b; MCC9-12.F.BF.4c)

How to FIND an Inverse How to VERIFY an Inverse x f(x)f(x)f(x)f(x) xf  1 (x) f(x) = 3x  2 x = 3y – x + 2 = 3y f  1 (x) = f () = 3( )  2 f (f  1 (x)) = 3( )  2 = x + 2 – 2 = x f(x) = f  1 (f(x) ) = = 3x 3 = x x (3x  2) © 2010, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia(MCC9-12.F.BF.4; MCC9-12.F.BF.4a; MCC9-12.F.BF.4b; MCC9-12.F.BF.4c)

(f + g)(x) = f(x) + g(x)(f - g)(x) = f(x) - g(x)(f g)(x) = f(x) g(x)(g o f)(x) = g(f(x)) g(x) = 3x + 2 f(x) = x 2 + 2x + 1 © 2010, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia(MCC9-12.A.APR.1; MCC9-12.A.APR.6)

+ - - (f + g)(x) = f(x) + g(x)(f - g)(x) = f(x) - g(x)(f g)(x) = f(x) g(x)(g o f)(x) = g(f(x)) g(x) = 3x + 2 f(x) = x 2 + 2x + 1 f(x) - g(x) = + = x 2 - x - 1 f(x) g(x) = (x 2 + 2x + 1) (3x + 2) f(x) ÷ g(x) = (x 2 + 2x + 1) (3x + 2) f(x) + g(x) =x 2 + 2x + 1 3x + 2 = x 2 + 5x + 3 x 2 + 2x + 1 3x + 2 x2x2 +2x+ 1 3x3x 3 +6x 2 +3x +2+2x 2 + 4x+ 2 = 3x 3 + 8x 2 + 7x+ 2 g(f(x)) = g(x 2 + 2x + 1) 3(x 2 + 2x + 1) + 2 3x 2 + 6x = 3x 2 + 6x © 2010, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia(MCC9-12.A.APR.1; MCC9-12.A.APR.6)