# section 2.6

```
Let f(x) = 3x – 1, g(x) = x2-4, then
(f + g)(x) = ______.
(write the function expression )

Given two functions f and g, suppose Domain
of f is Df, Domain of g is Dg
Sum
(f + g)(x) = f(x) + g(x)
Differenc
e
(f - g)(x) = f(x) – g(x)
Product
(fg)(x) = f(x)g(x)
F(x)
Quotient
(f/g)(x) = f(x) / g(x)
Domain:
Df intersect
Dg
Domain:
Df ∪ Dg,
where x such
that g(x) ≠ 0
f(x) = 3x -1 g(x) = x2 -4 h(x) = x + 2 p(x) = (x + 3)0.5
1.
2.
3.
4.
5.
6.
Evaluate: (f+g)(6);
Find (fh)(x);
Find (g - f)(x). Is this the same as (f - g)(x)?
Find (g / h)(x)
Find (h - p)(x)
Evaluate: (h - p)(1); (h - p)(-4)

Discussion
1, h(x) = x2 + 2x
(a) Find h(x + 1)
(a) Find h(x) + h(1)
2, f(x) = 3x + 5
(a) Find f(1/2)
(b) Find f(1) / f(2)

Example If possible, use the given representations of functions f
and g to evaluate (f + g)(4), (f - g)(-2), (fg)(1), and (f/g)(0)
f(x) = 2x + 1
g(x) = √ x
Step 1: Find domains of f and g
Step 2: Make sure the input is in the domain of f and g. If it is a
quotient operation,
make sure the denominator doesn’t equal to 0.
Step 3: Find corresponding expressions of operations
Step 4: Evaluate new generated functions

Consider a nonlinear function f and draw a
line through two points (x, f(x)) and
(x + h, f(x + h))
y
The slope of the line is:
y2 – y1
x2 – x1
B
=
f(x + h) – f(x)
(x + h) - x
= f(x + h) – f(x)
h
A
x
x+h
x
Difference Quotient

Example: Find and simplify the difference
quotient for the function f given by
f(x) = 3x2 + 2x

PG. 144: 1-4, 12-21(M3), 24, 33, 36, 75, 77,
78

KEY: 24, 36, 78
