Markville High School Combination of Functions in Depth Practice

Question Description

I’m working on a mathematics multi-part question and need an explanation to help me learn.

 

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1. Given the following, determine the domain for h(x) = f(x) + g(x):
a) 𝑓(𝑥) = log 𝑙𝑜𝑔 [− (𝑥 − 3)] 𝑎𝑛𝑑 𝑔(𝑥) =
b) 𝑓(𝑥) =
2
2𝑥−3
𝑎𝑛𝑑 𝑔(𝑥) =
𝑥
2. Given: 𝑓(𝑥) = 2 𝑎𝑛𝑑 𝑔(𝑥) =
− 𝑥 + 6+ 3
2
16 − 𝑥
− (𝑥 + 2) + 4
Graph: h(x) = (f + g)(x) over the domain of [-2, 3]
3. Given: 𝑓(𝑥) = 4 2𝑥 − 4
a) 𝑔𝑜𝑓(10)
−1
b) 𝑓[(𝑓𝑜𝑓 (4)]
c) x such that g(x) = 15
2
𝑔(𝑥) = 2𝑥 − 1
Determine:
4. If 𝑓(𝑥) =
1
2
2
2
9π − 𝑥 and 𝑔(𝑥) = 𝑥 , graph: (Please show ALL your work)
a) ℎ(𝑥) = (𝑓 𝑥 𝑔)(𝑥). (5 marks)
b) 𝑝(𝑥) = (𝑓 ÷ 𝑔)(𝑥).
(5 marks)
6. h(x) is a combined function of f(x) and g(x). Provide any two functions f(x) and g(x) and the combined function h(x)
such that the domain of h(x) is D={𝑥≤4, 𝑥≠ − 1, 𝑥∈𝑅}.

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Tags:
determining domains

combined function

arithmetic combination

real numbers

function composition

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