Download 6.1 Notes

WARM UP
Factor.
1) x2 – 3x – 4
2) x2 – 1
3) 2x2 + 3x + 1
4) 3x2 – 2x – 1

Operations on Functions
6.1
DOMAIN RESTRICTIONS


Only the functions that are rational will have
domain restrictions.
If there are no restrictions, the domain is all real
numbers.
EXAMPLE 1

A. Given f(x) = 3x2 + 7x and g(x) = 2x2 – x – 1,
find (f + g)(x).
EXAMPLE 1

B. Given f(x) = 3x2 + 7x and g(x) = 2x2 – x – 1,
find (f – g)(x).
EXAMPLE 2

A. Given f(x) = 3x2 – 2x + 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) = 3x2 – 2x – 1 and g(x) = x2 – 1,
find
EXAMPLE 3

A. Given f(x) = 2x2 + 3x – 1 and g(x) = x + 2,
find (f ● g)(x).
EXAMPLE 3
B. Given f(x) = 2x2 + 3x + 1 and g(x) = x2 – 3x – 4,
find
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) = 2x and g(x) = x2 – 3x + 2 and
h(x) = -3x – 4 then find each value.
a. f[g(3)]
b. g[h(-2)]
c. h[f(-4)]
WARM UP
If f(x) = 2x and g(x) = x2 and
h(x) = -5x – 4 then find each value.
a. f[g(3p)]
b. f[h(4s)]
EXAMPLE 5

Find [f ○ g](x) for
f(x) = 3x2 – x + 4 and g(x) = 2x – 1.
State the domain for each combined function.
EXAMPLE 6

Find [g ○ f](x) for

f(x) = 3x2 – x + 4 and g(x) = 2x – 1.

State the domain for each combined function.
EXAMPLE 7
Find [f ○ g](x) for
f(x) = -3x + 7 and g(x) = 5x3 – 8
State the domain for each combined function.
EXAMPLE 8
Find [g ○ f](x) for
f(x) = x2 + 2x – 3 and g(x) =
𝟏
𝒙
State the domain for each combined function.
EXAMPLE 9
Find [f ○ g](x) for
f(x) = x2 + 2x + 3 and g(x) =
𝟏
𝒙
State the domain for each combined function.
EXAMPLE 10

Hector has $100 deducted from every
paycheck for retirement. He can have this
deduction taken before state taxes are
applied, which reduces his taxable income.
His state income tax is 4%. If Hector earns
$1500 every pay period, find the difference
in his net income if he has the retirement
deduction taken before or after state taxes.