A rational number is a real number which can be written as the fraction of two integers. Which of the following shows a formally correct way to define the predicate Rational (x), which tells us that is rational? Rational (x): (Ey € I: 3 € I: x x = ²) Rational (x) → (VxER: Jy I: 32 € I: x = 1) OVER: ByI: 3 €I: Rational (x) + (x = 4) OVER: Rational (x) + (y I: 3 € 1 : x = 4)

Q: Which of the following expressions has a domain that is a subset of the domain (i.e. set of all…

A: We can find the domain of each function and then find the answer.

Q: Consider the function. 5x f(x) = √x² +1 Identify the domain of f. (Give your answer as an interval…

A:

Q: Find the values of a such that det (² 3-x 2 3-x 4 1 -1 -1-x = 0.

A: We have to find the value of x such thatWe know that

Q: Let f: Z → Z be defined as f(x)= >= { x + 9 √x+9 x-7 Find a formula for f-1. if x is odd if x is…

A:

Q: Find a number x such that x + 1 / x − 2 = 3x

A: The expression could be x+1x-2=3x or x+1x-2=3x. If the expression is x+1x-2=3x, then…

Q: A(-3,4) -5 54 -3 -2 -1 a.) Domain: b.) Range: c.) f (-3) = d.) f (0) = e.) f (x) = 4 when x = f.) f…

A:

Q: A8. (a) State (without proof) the Intermediate Value Theorem. (b) Use the Intermediate Value Theorem…

A:

Q: A and B are sets of real numbers defined as follows. A-(: |2> 2} B-(: |258} Write AnBand AUB using…

A: Solution:   Given that A & B are sets of real numbers such thatA = z | z>2B = z | z≤8

Q: If Xo and X, are two numbers with Xo F(X1) O B. F(XO) = F(X1) O C. None of the above O D. F(X0) <…

A: It depends on the conditions; If F is a increasing function then option D is correct. If F is…

Q: faノ= 4-ズ, と Finel!- ロん。 hf fes 2. on inverse 12] Domain fca) ?

A: Answer and explanation is given below...

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

A: This is the question from the topology.

Q: Let the domain of x be the set of negative real numbers. Then Vx, (1+ x² > 0) is a true statement a…

A:

Q: Let R be the set of real numbers, A = {x € R: 5<x< 10}, B = {r e R: 7<x<20}, C = (0, 10], D= (9,…

A:

Q: Which of the following constitute the values of the domain of f(x) Vx - 6? %3D A. all real values of…

A:

Q: F and H are sets of real numbers defined as follows. F={y|y21} H= {y |y>7} Write FUH and FnHusing…

A: A set is a well-defined collection of objects. The objects, which belong to the set, are called…

Q: If Xo and X, are two numbers with Xo < X, then the true one is

A: Answer:-  Option D is the correct answer.

Q: 1) Which set of values for x should be tested to determine the possible zeros of the function f (x)…

A: We need to find possible x values that needs to be checked where function is zero.   NOTE - As per…

Q: Let X be the number of hours spent studying on any given day. Which of the following is NOT true? A.…

A:

Q: Indicate if the function is bijective from R to R, f (x) = −3x + 4, justify your answer

A: Given f : R→R, f(x)=-3x+4 Here the function is linear function. f'(x)=-3&lt;0 for all x∈R Which…

Q: On the set of real numbers x2 + y2 = 1 Function. If x is a real number and y is an integer number:…

A:

Q: The value of x which satisfy 3x + 1| < - is : 5.

A:

Q: (5) Given f(x) -2r and h(x)= simplify using the following operations: Write answers in standard…

A:

Q: - Give the domain for k(a) in interval notation. x2 + 3x +2

A:

Q: Given the following radical function: P(t) = 5/2t – 4 +7 State the Domain of P(t) in interval…

A: Domain of the function

Q: Let Q denote the set of rational numbers. Show that card(Q)=x0. What is card(R/Q)?

A: Solution:- Step1:-      It is given that ℚ is the set of rational number  then,        we have to…

Q: Find the domain of the composite function fog. -5 12 f(x) =6 g(x) = %3D Ox #0, x z-2} Oxx #0, x -6,…

A: