6 1 Operations on Functions EXAMPLE 1 A

6. 1 Operations on Functions

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

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

EXAMPLE 2 A. Given f(x) = 3 x 2 – 2 x + 1 and g(x) = x – 4, find (f ● g)(x).

REMEMBER – YOU CANNOT HAVE A 0 IN THE DENOMINATOR OF A FUNCTION! B. Given f(x) = 3 x 2 – 2 x – 1 and g(x) = x 2 – 1, find

EXAMPLE 3

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 4 If f(x) = 2 x and g(x) = x 2 – 3 x + 2 and h(x) = -3 x – 4 then find each value. a. f[g(3)] b. g[h(-2)]

EXAMPLE 5 If f(x) = (2, 6), (9, 4), (7, 7), (0, – 1) and g(x) = (7, 0), (– 1, 7), (4, 9), (8, 2) , a) Find [f ○ g](x). b) Find [g ○ f](x).

EXAMPLE 6 Find [f ○ g](x) for f(x) = 3 x 2 – x + 4 and g(x) = 2 x – 1. State the domain and range for each combined function.

EXAMPLE 7 Find [g ○ f](x) for f(x) = 3 x 2 – x + 4 and g(x) = -2 x – 1. State the domain and range for each combined function.

EXAMPLE 8

EXAMPLE 9 If f(x) = axm and g(x) = bxn, perform the operation stated. A) f(x) g(x) B) f(g(x)) C) f(g(f(x)))