ADDITIONAL MATHEMATICS GRADE 10N WEEK 2 HOLIDAY WORK
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1. Functions 𝑓 and 𝑔 are defined for 𝑥 ∈ 𝑅, by 𝑓: 𝑥 → 5𝑥 − 2, 𝑔: → 2𝑥−1 , 𝑥 ≠ 2
i)
Find the value of 𝑔2 (2)
ii)
Find the value of 𝑥 for which
𝑎) 𝑓(𝑥) = 𝑓 −1 (𝑥)
b) 𝑓𝑔(𝑥) + 3𝑔(𝑥) = 0.
2. Function f and g are defined by
𝑓: 𝑥 → 4𝑥 − 17
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𝑔: 𝑥 →
,
𝑥 ≠ 3.5
2𝑥 − 7
𝑠𝑜𝑙𝑣𝑒 𝑡ℎ𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛
(𝑖)𝐹𝑖𝑛𝑑𝑓 2 (𝑥)𝑎𝑛𝑑 𝑔𝑓(7),
(ii). 𝑓 −1 (x) = 𝑔−1 (x)
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3. Functions f and g are defined by f(x) = 2𝑥+1, 𝑥 ≠ − 2 and g(x) = 2𝑥 + 3. Find
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(a) the value of x, given that fg(x) = 5,
(b) the values of x for which g(x) = f(x).
ADDITIONAL MATHEMATICS GRADE 10N WEEK 3 HOLIDAY WORK
1. Function f is defined by
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𝑓: 𝑥 → 5 − , 𝑥 ≠ 0
𝑥
𝑠𝑜𝑙𝑣𝑒 𝑡ℎ𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛
(𝑖)𝐹𝑖𝑛𝑑 𝑓 −1 𝑎𝑛𝑑 𝑠𝑡𝑎𝑡𝑒 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑥 𝑓𝑜𝑟 𝑤ℎ𝑖𝑐ℎ 𝑓 −1 𝑖𝑠 𝑢𝑛𝑑𝑒𝑓𝑖𝑛𝑒𝑑
(𝑖𝑖)𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒𝑠 𝑜𝑓 𝑥 𝑓𝑜𝑟 𝑤ℎ𝑖𝑐ℎ 𝑓(𝑥) = 𝑓 −1 (𝑥)
2𝑥
2. (a) Given that f(x) = 𝑥 2 −1 and g(x)=3x
(i)Find the domain of f(x)
(ii) fg(x)
(iii)Find g-1(2)
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3. A function h is defined as h(x) = 2x – 5, find
a) h(-4)
b) the value of x for which h(x)= 3
c) h-1(x)