Review of 1.4 (Graphing) Compare the graph with

1.5 Combinations of Functions

Arithmetic Combinations The sum, difference, product and quotient of two functions f and g are defined as follows. 1)Sum (f + g)(x) = f(x) + g(x) 2)Difference (f - g)(x) = f(x) - g(x) 3)Product (f * g)(x) = f(x) * g(x) 4)Quotient (f / g)(x) = f(x) / g(x)

Example 1. Let f(x) = x 2 + 3x -7, and g(x) = 4x +5. Find (f + g)(x),(f - g)(x),(f * g)(x),(f / g)(x) Now find (f + g)(3)

Example 2. Let f(x) = x 2 - 9, and g(x) = x - 3. Simplify the formula for f / g(x).

Composition of Functions The composition of two functions f and g is defined by (f ° g)(x) = f(g(x)). Example: Find and given that

Example Let f(x) = x 2 - x + 1, and g(x) = 3x - 2.