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If 𝑓(𝑔(𝑥))=cos(5𝑥+4), find the functions 𝑓(𝑥) and 𝑔(𝑥).Note: there may be more than one solution, but do not use the trivial solution 𝑔(𝑥)=𝑥.𝑓(𝑥)= 𝑔(𝑥)=

Question

If 𝑓(𝑔(𝑥))=cos(5𝑥+4), find the functions 𝑓(𝑥) and 𝑔(𝑥).Note: there may be more than one solution, but do not use the trivial solution 𝑔(𝑥)=𝑥.𝑓(𝑥)= 𝑔(𝑥)=

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Solution

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.

Please note that there are multiple solutions to this problem. This is just one possible solution.

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