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Zepler [3.9K]
3 years ago
8

#6 is the question, are these two functions inverse’s

Mathematics
1 answer:
olya-2409 [2.1K]3 years ago
8 0
I will find the inverse function of f(n) to see if it is g(n).

f(n) = 2(n - 2)^3

y = 2(x - 2)^3

x = 2(y - 2)^3

(y - 2)^3 = \dfrac{x}{2}

y - 2 = \sqrt[3]{\dfrac{x}{2}}

y = \sqrt[3]{\dfrac{x}{2}} + 2

y = \sqrt[3]{ \dfrac{x}{2} } \times \sqrt[3]{ \dfrac{4}{4}} + 2

y = \sqrt[3]{\dfrac{4x}{8}} + 2

y = \dfrac{ \sqrt[3]{4x }}{2} + 2

g(n) = \dfrac{\sqrt[3]{4n}} {2} + 2

The inverse function of f(n) is indeed g(n), so f(n) and g(n) are inverse functions.
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