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Composition of Functions

Composition of Functions. Learning Targets. Students will be able to find the composition of one function with another function. Function Composition. Notation. This does not say “FOG”. You read this “f of g of x”. Function Composition. Notation. Another way to write this is.

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Composition of Functions

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  1. Composition of Functions

  2. Learning Targets • Students will be able to find the composition of one function with another function

  3. Function Composition Notation This does not say “FOG” You read this “f of g of x”

  4. Function Composition Notation Another way to write this is OR f[g(x)]

  5. Function Composition Notation

  6. Function Composition OR EX 1: f(x) = x2 g(x) = x + 1 Start with g(x) and put that in to f(x) = (x + 1)2 = x2 + 2x + 1

  7. Function Composition EX 2: f(x) = x + 2g(x) = 4 – x2 Start with g(x) and put that in to f(x) = (4 – x2)+ 2 = -x2 + 6

  8. Function Composition EX 3: f(x) = x2 +1 g(x) = 2x Start with g(x) and put that in to f(x) = (2x)2+ 1 = 4x2 + 1

  9. evaluating with Function Composition (Numbers) EX 4: f(x) = x2 +1 g(x) = 2x Start with g(x) & find g(3). Put that answer in to f(x). g(3) = 6 f(6) = 37

  10. MORE Function Composition EX 5: f(x) = x2 - 4 g(x) = 4x - 1 • f[g(-1)] • g(f(2)) • f[g(a + 1)] g(-1) = -5; f(-5) = 21 f(2) = 0;g(0) = -1 g(a+1)= 4(a+1)-1 = 4a+3; f(4a+3) = (4a+3)2 – 4 = 16a2+24a+5

  11. 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

  12. 6) For what values of “x” isf(g(x)) = 10 Given: f(x) = 2x and g(x) = x + 3 Start from the outside. Set f(x); 2x = 10 and solve. Check by seeing if: f(g(2)) = 10 So x = 5. This means that g(x) = 5. x + 3 = 5; therefore x = 2

  13. Homework • Composition of Functions Worksheet

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