Enter a T or an F in each answer space below to indicate whether the correspondi
ID: 2880674 • Letter: E
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 ratio of two odd functions is odd The composition of an odd function and an odd function is even A function cannot be both even and odd. The sum of an even and an odd function is usually neither even or odd, but it may be even. The sum of two even functions is even The product of two even function is even The product of two odd function is odd The composition of an even and an odd function is even All of the answers must be correct before you get credit for the problem.Explanation / Answer
Let f (x) be a real-valued function of a real variable. Then f is even if the following equation holds for all x in the domain of f
f(-x)=f(x)
Let f (x) be a real-valued function of a real variable. Then f is odd if the following equation holds for all x in the domain of f
f(-x)=-f(x)
Let f(x)=x^2 is even function and g(x)=x^3 is a odd function
1) Let two odd functions as g1(x)=x^3,g2(x)=x^5
g1(x)/g2(x) =x^3/x^5 =1/x^2 is an even function
The ratio of two odd functions is odd is False F
2) Let two odd functions as g1(x)=x^3,g2(x)=x^5 implies g1o(g2(x))=g1(x^5)=(x^5)^3 is odd function
The composition of an odd function and an odd function is even is False F
3)The only function which is both even and odd is the constant function which is identically zero
f(x)=0 for all x
A function cannot be both even and odd is False F
4)The sum of an even and odd function is neither even nor odd, unless one of the functions is identically zero
Let f(x)=x^2 is even function and g(x)=x^3 is a odd function
f(x)+g(x)=x^2+x^3 is neither even or odd
Let f(x)=0 is even function and g(x)=x^3 is a odd function
f(x)+g(x)=0+x^3=x^3 is odd function
Let f(x)=0 is odd function and g(x)=x^2 is an even function
f(x)+g(x)=0+x^2 is an even function
The given statement is true T
5) Let f(x)=x^2 is an even function and g(x)=x^4 is an even function
f(x)+g(x)=x^2+x^4 is an even function
The sum of two even functions is even function is True T
6) Let f(x)=x^2 is an even function and g(x)=x^4 is an even function
The product of two even function is f(x)*g(x)=x^2*x^4=x^6
The product of two even function is even is True T
7) Let f(x)=x is an odd function and g(x)=x^3 is an odd function
The product of two odd function is f(x)*g(x)=x*x^3=x^4 is an even function
The product of two odd function is odd is False F
8) Let f(x)=x^2 an even function and g(x)=x is an odd function
fog(x)=f(g(x))=f(x)=x^2 is an even function
The composition of an even function and an odd function is even is True T
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