If f(x) is an even function and g(x) is an odd function, which of the following must be even?I. f(g(x))II. f(x) + g(x)III. f(x)g(x)
Question
Solution 1
To determine which of the given expressions must be even, we need to use the properties of even and odd functions.
- f(g(x)):
- Since ( g(x) ) is an odd function, ( g(-x) = -g(x) ).
- Since ( f(x) ) is an even function, ( f(-x) = f(x) ).
- Therefore, ( f(g(-x)) = f(-g(x)) = f Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob
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