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Lesson 2-8: Operations of Functions

Lesson 2-8: Operations of Functions. Advanced Math Topics. Operations with functions. (f + g)(x)= f(x) + g(x) Add the functions (f – g )(x) = f(x) – g(x) Subtract the functions (be sure to subtract all parts of the second function and not just the first part)

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Lesson 2-8: Operations of Functions

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  1. Lesson 2-8: Operations of Functions Advanced Math Topics

  2. Operations with functions • (f + g)(x)= f(x) + g(x) Add the functions • (f – g )(x) = f(x) – g(x) Subtract the functions (be sure to subtract all parts of the second function and not just the first part) • (f · g)(x) = f(x) · g(x) Multiply the functions (foil/distribute) • (f/g)(x) = f(x) / g(x), g(x) cannot = 0 Divide the functions (factor if possible and simplify)

  3. Examples • f(x)= x2 – 3x + 1 and g(x) = 4x + 5 find • (f + g) (x) and (f – g)(x)

  4. Example • f(x) = x2 + 5x – 1 and g(x) = 3x – 2 find • (f · g)(x) and (f/g)(x)

  5. Composition of Functions • [f o g](x) = f[g(x)] • Plug in the entire second function for every x then simplify

  6. Example • Find [f o g](x) and [g o f](x) for f(x) = x+3 and g(x) = x2 + x – 1 • Evaluate [f o g](x) and [g o f](x) for x = 2

  7. Find the sum, difference, product and quotient of f(x) and g(x) f(x) = x2 + 3 g(x) = x - 4

  8. If f(x) = 3x, g(x) = x + 7 amd h(x) = x2 find the following • f[g(3)] • g[h(-2)] • h[h(1)]

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