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Composition of Functions Section 1-8

Composition of Functions Section 1-8. Objectives. I can 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. OR f[g(x)].

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Composition of Functions Section 1-8

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  1. Composition of FunctionsSection 1-8

  2. Objectives • I can 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 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. MORE Function Composition EX 6: f(x) = |x| g(x) = x3 - 2 • [f o g](x) • (g o f)(x) • (f o g)(-2) |x3 – 2| |x|3 - 2 10

  13. 7) 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

  14. Homework • WS 2-2

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