1. Operations on Functions
6.1
Operations on Functions

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

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

5. Example 2
A. Given f(x) = 3x2 – 2x + 1 and g(x) = x – 4, find (f ● g)(x).

6. Remember – you cannot have a 0 in the denominator of a function!
Given f(x) = 3x2 – 2x – 1 and g(x) = x2 – 1,
find

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

8. 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.

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

10. 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).

11. WARM UP
If f(x) = {(1, 2), (0, –3), (6, 5), (2, 1)} and g(x) = {(2, 0), (–3, 6), (1, 0), (6, 7)}, find a. f ○ g = b. g ○ f =

12. Example 6 Find [f ○ g](x) for f(x) = 3x2 – x + 4 and g(x) = 2x – 1.
State the domain and range for each combined function.

13. Example 7 Find [g ○ f](x) for f(x) = 3x2 – x + 4 and g(x) = -2x – 1.
State the domain and range for each combined function.

14. Example 8 Find [f ○ g](x) for
h(x) = x2 + 2x + 3 , f(x) = 𝟏 8x + 9 and g(x) = x + 5.
State the domain and range for each combined function.

15. 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)))