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Thursday Last Day for Test corrections Retest 7:40am tomorrow Thursday: Factor these 3 problems 27 x 8 3 9 x 36 x 4 x 16 3 x 81 4 2 Factor these 3 problems 27 x 8 3 (3x 2)(9 x 6 x 4) 2 Factor these 3 problems 9 x 36 x 4 x 16 3 2 (3x 2)(3x 2)( x 4) Factor these 3 problems x 81 4 ( x 9)( x 3)( x 3) 2 Composition of Functions Section 1-8 Objectives I can find the composition of one function with another function Function Composition Notation ( f g )( x) This does not say “FOG” You read this “f composed with g of x” Function Composition Notation ( f g )( x) Another way to write this is f ( g ( x)) OR f[g(x)] Function Composition Notation ( f g )( x) INSIDE function 1st OUTSIDE function last Function Composition ( f g )( x) OR f ( g ( x)) EX 1: f(x) = x2 Start with g(x) and put that in to f(x) g(x) = x + 1 = (x + 1)2 = x2 + 2x + 1 Function Composition ( f g )( x) EX 2: f(x) = x + 2 g(x) = 4 – x2 Start with g(x) and put that in to f(x) = (4 – x2) + 2 = -x2 + 6 Function Composition ( f g )( x) EX 3: f(x) = x2 + 1 Start with g(x) and put that in to f(x) g(x) = 2x = (2x)2 + 1 = 4x2 + 1 evaluating with Function Composition (Numbers) ( f g )(3) EX 4: f(x) = x2 + 1 Start with g(x) & find g(3). Put that answer in to f(x). g(x) = 2x g(3) = 6 f(6) = 37 MORE Function Composition EX 5: f(x) = x2 - 4 g(x) = 4x - 1 a) f[g(-1)] g(-1) = -5; f(-5) = 21 b) g(f(2)) f(2) = 0; g(0) = -1 c) f[g(a + 1)] g(a+1)= 4(a+1)-1 = 4a+3; f(4a+3) = (4a+3)2 – 4 = 16a2+24a+5 MORE Function Composition EX 5: f(x) = x2 - 4 g(x) = 4x - 1 d) [f o g](x) g(x) = 4x – 1 so put this into f(x) for x (4x – 1)2 - 4 16x2 – 8x - 3 6) For what values of “x” is f(g(x)) = 10 Given: f(x) = 2x and g(x) = x + 3 Start from the outside. Set f(x); 2x = 10 and solve. So x = 5. This means that g(x) = 5. x + 3 = 5; therefore x = 2 Check by seeing if: f(g(2)) = 10 Homework WS 2-4