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Function notation and operation

Function notation and operation. f(x). F is the name of the function. X is the input for the function. (input, ?) What does f(x) = ? (input, output). Adding and subtracting functions. (f + g)(x) = f(x) + g(x) (f - g)(x) = f(x) - g(x ) f(x) = 3x + 2 and g(x) = 6 - 2x

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Function notation and operation

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  1. Function notation and operation

  2. f(x) • F is the name of the function. • X is the input for the function. • (input, ?) • What does f(x) = ? • (input, output)

  3. Adding and subtracting functions • (f + g)(x) = f(x) + g(x) • (f - g)(x) = f(x) - g(x) • f(x) = 3x + 2 and g(x) = 6 - 2x (f + g)(x) = f(x) + g(x) = (3x + 2) + (6 - 2x) = x + 8 (f - g)(x) = f(x) - g(x) = (3x + 2) - (6 - 2x) = 5x - 4

  4. Multiplying and dividing functions • (f g)(x) = f(x) g(x) • (f /g)(x) = f(x) /g(x) • f(x) = 3x + 2 and g(x) = 6 - 2x (f  g)(x)=f(x)  g(x)=(3x + 2)(6 - 2x)=-6x2+14x + 12 (f / g)(x) = f(x) / g(x)= (3x + 2)/(6 - 2x);x≠3

  5. f(x) = x-2y and g(x) = x+y • Find (f + g)(x), (f -g)(x), (f g)(x), (f / g)(x) (f + g)(x) = f(x) + g(x) = (x-2y) + (x+y) = 2x -y (f - g)(x) = f(x) - g(x) = (x-2y) - (x+y) = -3y (f  g)(x)=f(x)  g(x)=(x-2y)(x+y)=x2 - xy -2y2 (f / g)(x) = f(x) / g(x)= (x-2y)/(x+y);x+y≠3

  6. Homework: find (f + g)(x), (f - g)(x), (f  g)(x), (f / g)(x) • f(x) = m + n and g(x) = n – 3m • f(x) = ½ m and g(x) = 4m • f(x) = x + 2 and g(x) = x • f(x) = 3(m + n) and g(x) = n – 3m • f(x) = x/2 and g(x) = 2/x

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