Choose from below the correct response:
"If a function g is an even function, then the composition function $f\circ g$ f\circ g is even for any function f."
This statement is:

Question

Choose from below the correct response: "If a function   g  is an even function, then the composition function   f\circ g  is even for any function   f ." This statement is:

Accepted Answer

True because   f(g(-x)) = f(g(x))  for all   x  in the domain of   g , as   g  is an even function.

Answer

True because when   g(x)=x^2  we have   g(-x) = (-x)^2  which is equal to   g(x) .

Answer

it will depend on the functions   f  and   g .

Answer

False because   g(-x) = -g(x) , thus   f(g(-x)) = f(-g(x))  which is only equal to   f(g(x))  when   f  is even.

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Choose from below the correct response: "If a function g is an even function,...

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