Lesson 1.5
Read: Pages 62-68
Page 58: #1-29 (EOO), 37-61 (EOO)
Combinations of Functions
Objective
Students will know how to find arithmetic combinations
and compositions of functions.
Use the graph of f and g to graph h(x)=(f + g)(x).
Find (a) (f + g)(x) (b) (f - g)(x) (c) (fg)(x)
and (d) (f/g)(x). What is the domain of f/g?
Use a graphing utility to graph the functions f, g,
and h in the same viewing window.
Find (a) f  g , (b) g  f, and, if possible,
(c) ( f  g )(0)
𝑓 𝑥 = 3𝑥 + 5
𝑔 𝑥 = 𝑥3 + 1
Determine the domains of (a) 𝑓, (b) 𝑔, and
(c) f  g . Use a graphing utility to verify
your results.
𝑓 𝑥 = 𝑥+3
𝑥
𝑔 𝑥 =
2
3
𝑓 𝑥 = 2
𝑥 −1
𝑔 𝑥 =𝑥+1
Find (a) 𝑓(𝑔 𝑥 ), 𝑔(𝑓 𝑥 ), and the domain of
𝑓 𝑔 𝑥 . Determine algebraically whether
𝑓 𝑔 𝑥 = 𝑔(𝑓 𝑥 ). (b) Use a graphing utility to
graph 𝑓(𝑔 𝑥 ) and 𝑔(𝑓 𝑥 ) and complete a table of
values to confirm 𝑓 𝑔 𝑥 = 𝑔(𝑓 𝑥 ).
𝑓 𝑥 =
1
𝑥4
𝑔 𝑥 = 𝑥4
𝑓 𝑥 = 𝑥3 − 4
𝑔 𝑥 =
3
𝑥 + 10
Use the graphs of f and g to evaluate the functions.
(𝑓 − 𝑔)(1)
(𝑓𝑔)(4)
( f  g )(1)