Ifย ๐‘“(๐‘”(๐‘ฅ))=cos(5๐‘ฅ+4), find the functions ๐‘“(๐‘ฅ) and ๐‘”(๐‘ฅ).Note: there may be more than one solution, but do not use the trivial solution ๐‘”(๐‘ฅ)=๐‘ฅ.๐‘“(๐‘ฅ)= ๐‘”(๐‘ฅ)=

Question

Ifย ๐‘“(๐‘”(๐‘ฅ))=cos(5๐‘ฅ+4), find the functions ๐‘“(๐‘ฅ) and ๐‘”(๐‘ฅ).Note: there may be more than one solution, but do not use the trivial solution ๐‘”(๐‘ฅ)=๐‘ฅ.๐‘“(๐‘ฅ)= ๐‘”(๐‘ฅ)=
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Solution 1

The question is asking to find the functions f(x) and g(x) such that f(g(x)) = cos(5x+4).

One possible solution could be:

f(x) = cos(x) g(x) = 5x + 4

This is because if you substitute g(x) into f(x), you get f(g(x)) = cos(5x+4), which is the original function.

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