The graph of a power function y = kxº is given below. (Assume that the exponent is an integer.) Which of the following statements about k and p is true? O A) k is positive and p is odd B) k is positive and P is even O C) k is positive and P is negative D) k is negative and p is even

Q: Are the following functions? es, and roots Find b x\y 7|3 xly 1|7 xly 713 714 312 1|2 xly 1|7 314…

A: If there is more than one value of y for one x, then the relation is not a function. For this, for…

Q: following must be true?

A: As per the definition of function if f(a) = f(b) then a must be equal to b.   In given question f(a)…

Q: d) Is the composition of two one-one functions a one-to-one function? e) Is it true that P(A) ≤ A?

A: For part (d), the answer is YES.

Q: 3. Let a, b, c, d be real numbers with a < b and c < d. Find a one-to-one correspondence between (a,…

A:

Q: . Let a be a positive number. Prove that for each real number x there is an integer n such that na <…

A:

Q: Determine whether the following statements are True or False: a - For all relations R and S, ROS=SOR…

A: We solve this using counter examples .

Q: If R is an integer domain, show that it contains exactly two elements a that satisfy a? = a.

A: Given R is an integral domain. We have to show that it contains exactly two elements a that satisfy…

Q: |a|, called the of a, represents the distance from on the number line. to

A: It is known that a represents the absolute value if a.

Q: Consider a ruler that takes as input any integer z and outputs. Is r a function? Why?

A: Given that r takes input as integer z and outputs Here the input is different while the output is…

Q: Prove the statement if it is true, and give a counterexample if it is not true. a. For every real…

A: Both the subparts are solved with explanation.

Q: From the statements below select the correct ones. O For sets A and B, if A B then A| B|. O If there…

A: We have to choose the correct statements.

Q: Activity 7.2. Even if we omit the negatives, the real numbers fail to satisfy the well-ordering…

A: Given that the set R+ of all positive real numbers fails to be well ordered.

Q: .18 Let x, a and 8 be real numbers. Show that the statements |x-al < 8 and a -8 < x < a +8 are…

A:

Q: Evaluate the following commutators [Â, B] = ÂB – BÂ. Hint: use an arbitrary function that cancels at…

A: a x,PxPx=-ih∂∂xx,Pxφ=x,-ih∂∂xφ=-ihx∂φ∂x+ih∂∂xxφ=-ihx∂φ∂x+ih∂φ∂x+ihφ=ihφ∴x,Px=ih

Q: 10. Σ = {(1,3), (-∞, 2), (0, ∞0), (-∞,4)}

A: This is the question from the topology.

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Q: For a real number a, if a + 0 then a x a E R+.

A:

Q: Input Output 6. 7 3 8. 10 6. Function: 2. 4.

A: On solving, we get

Q: A. Describe the error in the following: a. 5 is a subset of N b. x>1 and x 1<4 c. Given the function…

A: A. a. ) 5 is not a subset of N, its an element of N. It should be written as {5} is a subset of N.…

Q: 7.5. Let IR denote the set of all real numbers. Describe R x R.

A:

Q: y = x6 One -to- One function Not one -to- One function 2 No one of them 3

A: Let's find given function is one to one function or not.

Q: O A В D All of the Above C

A: From the given graph find out which function has a domain of all real numbers

Q: 1. State the properties of the Bassel function.

A: Here are some properties of Bassels Function

Q: Prove the following:  If a <b, then -b < -a

A:

Q: Suppose that x is a real number and that UCR. Prove that the following two conditions are…

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Q: Let a be a real number. If lim, »0 47 = 8, VIta-Vā then which of the followings is the value of a?

A:

Q: The functions h and m are defined on the set R of real numbers by h:x→ ax +b and m:x → cx -d, where…

A:

Q: Q3 (Recall the notation: For any set S CR and any k eR, kS = {ks : sE S}.) (a) Someone has claimed…

A: We will use the fact that the set of integers is countable and every subset of a countable set is…

Q: b. The functions g and h are defined by g: x→x2 – 4 and f: x . where x is a 2-x real number. i.…

A: Domain or rational function of the form f(x)/g(x) is the set R- {x:g(x)=0}.

Q: Let f be a function from R to R. Without using words of negation, write the meaning of “f is not an…

A: What is Statement: Any style of reasoning starts with a mathematical assertion. A mathematical…