Enter a T or an F in each answer space below to indicate whether the correspondi

Question

Enter a T or an F in each answer space below to indicate whether the corresponding statement is true or false. You must get all of the answers correct to receive credit. The sum of an even and an odd function is usually neither even or odd, but it may be even. The product of two even functions is even The composition of an odd function and an odd function is even The ratio of two odd functions is odd The product of two odd functions is odd The composition of an even and an odd function is even The sum of two even functions is even A function cannot be both even and odd.

Explanation / Answer

Answers

1.False ,unless one of the functions is equal to zero over the given domain.

2.True, f and g are even functions ,f(-x)=f(x) and g(-x)=g(x) implies that product is even.

3.False

4.False, f(x) and g(x) are odd functions ,(f/g)(-x)=f(-x)/g(-x)=-f(x)/-g(x)=(f/g)(x),f/g is even.

5.False, f(x) and g(x) are odd functions ,f(-x)g(-x)=(-f(x))(-g(x))=f(x)g(x), the product is even.

6.True

7.True

8.True ,Yes the function cannot be both at the same time provided f(x) not equal to zero.

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