Operations on Functions Day 1 – Add, Subtract, Multiply and Divide 6.1 Operations on Functions Day 1 – Add, Subtract, Multiply and Divide

Example 1 A. Given f(x) = 3x2 + 7x and g(x) = 2x2 – x – 1, find (f + g)(x).

B. Given f(x) = 3x2 + 7x and g(x) = 2x2 – x – 1, find (f – g)(x).

Example 2 A. Given f(x) = 3x2 – 2x + 1 and g(x) = x – 4, find (f ● g)(x). Find the domain for the combined function

Remember – you cannot have a 0 in the denominator of a function! B. Given f(x) = 3x2 – 2x + 1 and g(x) = x – 4, find Then find the domain for the combined function

C. Given f(x) = 2x2 + 3x – 1 and g(x) = x + 2, find C. Given f(x) = 2x2 + 3x – 1 and g(x) = x + 2, find . Find the domain for each combined function

Operations on Functions Day 2 – Composite Functions 6.1 Operations on Functions Day 2 – Composite Functions

Composite Functions Another way to combine functions is a composition of functions. In a composition of functions, the results of one function are used to evaluate a second function.

Example 3 B. Find [f ○ g](x) and [g ○ f](x) for f(x) = 3x + 4 and g(x) = 2x – 1. State the domain for each combined function.

B. Find [f ○ g](x) and [g ○ f](x) for f(x) = 3x2 – x + 4 and g(x) = 2x – 1. State the domain for each combined function.

Example 4: If f(x) = 2x, g(x) = x2 – 3x + 2, and h(x) = -3x – 4 then find each value. f[g(3)] g[h(-2)] h[f(-4)]