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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