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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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Presentation on theme: "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 +"— Presentation transcript:

1 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 + 2 3 © 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)

2 How to FIND an Inverse How to VERIFY an Inverse x f(x)f(x)f(x)f(x) 5 0-2 24 37 xf  1 (x) 5 -20 42 73 f(x) = 3x  2 x = 3y – 2 +2 +2 x + 2 = 3y 3 3 3 3 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 + 2 3 (3x  2) + 2 3 © 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)

3 (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)

4 + - - (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 + 3 + 2 = 3x 2 + 6x + 5 - © 2010, Dr. Jennifer L. Bell, LaGrange High School, LaGrange, Georgia(MCC9-12.A.APR.1; MCC9-12.A.APR.6)

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Domain: 1) f(0) = 8 2) f(3) = 3) g(-2) = -2 4) g(2) = 0 5) f(g(0)) = f(2) =0 6) f(g(-2)) = f(-2) =undefined 7) f(g(2)) = f(0) =8 8) f(g(-1)) = f(1) =3.
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