1. Function Operations Function Composition

2. Function Operations Given f(x) = 2x2 + 1 and g(x) = 5x – 3
1.Find (f + g)(x) and give the domain. This could be written f(x) + g(x).
2. Find (f – g)(x) and give the domain. This could be written f(x) – g(x)

3. Function Operations
Given f(x) = 2x2 + 1 and g(x) = 5x – 3 1.Find f(x) ∙ g(x) and give the domain. Could be written (f ∙g)(x). 2. Find f(x)/g(x) and give the domain. Could be written (f/g)(x).

4. Function Composition
Function Composition is just fancy substitution, very similar to what we have been doing with finding the value of a function.
The difference is we will be plugging in another function.

5. Function Composition
Just the same we will still be replacing x with whatever we have in the parentheses.
The notation looks like g(f(x)) or f(g(x)).
We read it ‘g of f of x’ or ‘f of g of x’

6. Function Composition
You will see (x) which is the same as f(g(x)) and (x) which is the same as g(f(x)).

7. Function Composition EXAMPLE Given f(x) = 2x + 2 and
g(x) = 2, find f(g(x)).

8. Function Composition
Given g(x) = x - 5 and f(x) = x + 1, find f(g(x)) and g(f(x). Give the domain.

9. Function Composition
Given f(x) = x2 + x and g(x) = x - 4, find f(g(x)) and g(f(x)). Give the domain.

10. Function Composition
Given f(x) = x2 + x and g(x) = x - 4, find f(g(x)) and g(f(x)). Give the domain.

11. Function Composition
Given f(x) = 2x + 5 and g(x) = 8 + x, find f(g(-5)).

12. Function Composition
Given f(x) = 2x + 5 and g(x) = 8 + x, find g(f(-5)).