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Adding, Subtracting Functions

As well as Multiplying and Dividing Them!

Adding and Subtracting Functions

There is nothing tricky about adding or subtracting functions. To add, or subtract, functions, first evaluate the given functions then perform the indicated operation.
    Example Problem
  • f(x) = 2x
  • g(x) = 3x+1
  • What is f(3) + g(4) ?
  • Step 1: evaluate the individual functions
    • f(3)  = 2×3 = 6
    • g(4) = 3×4 +1 = 13
  • Step 2: Add the values that your functions produced
    • f(3) + g(4) = 6 + 13 = 19
Practice Problems
Functions:
f(x) = 3x-1
g(x) = 3x3-1
Evaluate f(6) + g(2)
Answer
Functions:
f(x) = 4x – 1
g(x) = x2
Evaluate f(5) - g(3)
Answer

Multiplying and Dividing Functions

Multiplying and Dividing functions works the same as adding and subtracting functions. Simply evaluate the individual functions then perform the indicated multiplication or division.
Example Problem
  • f(x) = 3x
  • g(x) = 5x+2
  • What is f(8) ÷ g(2) ?
  • Step 1: evaluate the individual functions
    • f(8)  = 3 × 8 = 24
    • g(2) = 5 ×2 +2 = 12
  • Step 2: Divide the values that your functions produced
    • f(8) ÷ g(2) = 24 ÷ 12 = 2
  • Practice Problems
    Functions:
    j(x) = 5x
    p(x) =x+1
    Evaluate j(7) ÷ p(4)
    Answer
    Functions:
    f(x) = 3x+2
    k(x) = 5x+1
    Evaluate f(4) × k(2)
    Answer