3.6-1 Combining Functions

If we have multiple functions, we can combine them/evaluate them at values, to produce a single value The combination can be produced by just using numbers

Addition/Subtraction Let f and g be two functions A) (f + g) (x) = f(x) + g(x) Ex. (f + g) (1) = f(1) + g(1) B) (f – g) (x) = f(x) – g(x) Ex. (f – g) (-1) = f(-1) – g(-1)

Multiplication/Division Let f and g be two functions C) (fg) (x) = f(x)g(x) Ex. (fg) (-3) = f(-3)g(-3) D) (f/g)(x) = f(x)/g(x) Ex. (f/g)(5) = f(5)/g(5)

We do not necessarily need to know the actual function We just need to know the function values for f(x) and g(x) Graphs Sets of ordered pairs Function itself Values for f(x) and g(x)

Example. Given that f(-3) = 15 and g(-3) = -4, find: 1) (f + g)(-3) 2) (f – g)(-3) 3) (fg) (-3) 4) (f/g)(-3)

Example. Given the following, find (fg)(-3) and (f + g)(-3).

Finding Formulas If we need to find a new formula, we simply will look to combine the functions using the correct operation Distribute Check for properties of exponents Combine like terms

Example. Find the formula and domain for (f + g) and (f/g) given the following two functions. f(x) = x – 3 g(x) = x2

Example. Evaluate (f + g)(10) and (fg)(1) given the following two functions. f(x) = 1/x2 g(x) = 2x + 3

Assignment Pg. 269 1-29 odd