# 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) ๐(๐ฅ) = log ๐๐๐ [โ (๐ฅ โ 3)] ๐๐๐ ๐(๐ฅ) =
b) ๐(๐ฅ) =
2
2๐ฅโ3
๐๐๐ ๐(๐ฅ) =
๐ฅ
2. Given: ๐(๐ฅ) = 2 ๐๐๐ ๐(๐ฅ) =
โ ๐ฅ + 6+ 3
2
16 โ ๐ฅ
โ (๐ฅ + 2) + 4
Graph: h(x) = (f + g)(x) over the domain of [-2, 3]
3. Given: ๐(๐ฅ) = 4 2๐ฅ โ 4
a) ๐๐๐(10)
โ1
b) ๐[(๐๐๐ (4)]
c) x such that g(x) = 15
2
๐(๐ฅ) = 2๐ฅ โ 1
Determine:
4. If ๐(๐ฅ) =
1
2
2
2
9ฯ โ ๐ฅ and ๐(๐ฅ) = ๐ฅ , graph: (Please show ALL your work)
a) โ(๐ฅ) = (๐ ๐ฅ ๐)(๐ฅ). (5 marks)
b) ๐(๐ฅ) = (๐ รท ๐)(๐ฅ).
(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={๐ฅโค4, ๐ฅโ  โ 1, ๐ฅโ๐}.

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Tags:
determining domains

combined function

arithmetic combination

real numbers

function composition

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