Given f: [] → R where f(x) = sin x Is it a function or not? If function, identify whether it is one-to-one but not onto, onto but not one-to-one, a one-to-one correspondence, or neither one-to-one nor onto. Else, select not a function.

Q: Is there a function that is both even and odd?

A: Yes, f(x)=0 is both even and odd.

Q: Each function f is defined as f : R - R. Prove why each of the functions is one to one or not one to…

A: See the attachment

Q: Let f be a function from the set A to B. Let S and T be subsets of A. Show that f-1(S intersection…

A:

Q: For a function f: A --> B and subsets C and D of A and E and F of B, prove the following: f-1(E -…

A:

Q: B Evaluate the piecewise function f at the given x-values. Write the answer using function notation…

A: In the given graph, the bold line indicates the function. The open circle is not included in the…

Q: let f be the function x²-C for x< 5 flx)=3x+5c for X Z 5

A:

Q: Each function f is defined as f :R +R. Prove why each of the functions is one to one or not c one.…

A: We will check the one to one of these functions

Q: Formulate a condition for f to be symmetric with respect to the point (a, 0) on the x-axis.

A:

Q: et f: x imply y be some function. Suppose 3 belongs to Y. What can you say about the inverse…

A: Given that  f : X→Y is a function.  The domain of the function f : dom f=X The range of the function…

Q: Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a functionfrom A to B.…

A: givenA = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a functionfrom A to B

Q: Let f be the function from {a, b, c, d, e} to {1,2,3,4} with ƒ(a) = 3, ƒ (b) = 1, f(c) = 2, f(d) = 4…

A:

Q: Determine whether the given statement is true or false. If the statement is false, make the…

A: To determine: The given statement is true or false,  "Prove that if f and g are even functions, then…

Q: Let f be a function. If f (a) = f (6), then a = b. O True O False

A: We have to check is true or not

Q: Let f be a function. Then f (a) + f (b) = f (a + b) . O True O False

A: We need to proveor disprove if  fa+fb=fa+b

Q: Nap Lajoie has a lifetime batting average of 0.338. Assume that Nap Lajoie came to bat officially…

A: Given : Nap Lajoie has a lifetime batting average of 0.338 and came to bat officially six times…

Q: Let f be a function of x. Which of the following statements, if true, would guarantee that there is…

A:

Q: Let A = {x, y} and B = {w,z}. Describe all relations from A to B. Indicate which of these are…

A:

Q: Consider the possible functions from [7] to [9].  How many in which f-1 is not a functio

A: Let f:7→9 is a function then, Let A=[7] and B=[9] So, n(A)=7 and n(B)=9 Now, the total functions of…

Q: Determine if the following relations describe a function. Justify your answer. a.) R₁ = {(-2,0),…

A:

Q: [9] Let A = {a, b, c, d} and B = {1, 2, 3}. Define a function F: A → B as follows: F3(а, 3), (b, 3),…

A:

Q: Why is it important to determine the domain of f beforegraphing f ?

A: Domain of a function: The set of values of input of a function for which output of the function…

Q: Assume that the relation x = √500+ 5y² defines y implicitly as a function of x. Determine y" as a…

A:

Q: Given f: R → R where f(x) = x³ Is it a function or not? If function, identify whether it is…

A:

Q: Explain why a function that is not one-to-one on an interval I cannot have an inverse function on I.

A: Inverse of a function is possible if function is one-to-one. A function is said to be one-to-one if…

Q: . F(2) — /(-2) b. F(-1)/(-2) с. —2/(-

A:

Q: :N N amd 9: N-oN are functions such that f is not onto but f+9 is onto Prove that 9 is onto or give…

A: Suppose that f:ℕ→ℕ and g:ℕ→ℕ are functions such that f is not onto but f+g is onto. To prove that g…