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Adding, subtracting and multiplying functions worksheets Grade 10

Find (f + g)(x), (f − g)(x) and (fg)(x), then simplify.

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How to do it

(f + g)(x) = f(x) + g(x), (f − g)(x) = f(x) − g(x), and (fg)(x) = f(x) · g(x). Combine like terms.

f(x)=−4x+9,g(x)=x−8;(fg)(x)=−4x2+41x−72f(x) = -4x + 9,\quad g(x) = x - 8;\quad (\text{fg})(x) = -4x^{2} + 41x - 72
(fg)(x)=(−4x+9)(x−8)=−4x2+41x−72(\text{fg})(x) = (-4x + 9)(x - 8) = -4x^{2} + 41x - 72multiply each term of f(x) by each term of g(x)

Example problems

  1. f(x)=−x−3,g(x)=−3x2+6x−2;(f−g)(x)=f(x) = -x - 3,\quad g(x) = -3x^{2} + 6x - 2;\quad (f - g)(x) =
  2. f(x)=−5x+3,g(x)=x2−4x−9;(f−g)(x)=f(x) = -5x + 3,\quad g(x) = x^{2} - 4x - 9;\quad (f - g)(x) =
  3. f(x)=5x+6,g(x)=4x+5;(fg)(x)=f(x) = 5x + 6,\quad g(x) = 4x + 5;\quad (\text{fg})(x) =
  4. f(x)=−5x−4,g(x)=4x−4;(f+g)(x)=f(x) = -5x - 4,\quad g(x) = 4x - 4;\quad (f + g)(x) =

Functions

  1. Evaluating functions
  2. Finding the domain of a function
  3. Adding, subtracting and multiplying functions
  4. Composition of functions
  5. Inverse functions
  6. Transformations of functions
  7. Even and odd functions
  8. Average rate of change