2. Let : RR and y: R+ → R be mappings with 6(x) -2e-x. (a) Find the range of y. = 1. Use your answer to determine whether y is surjective. (b) Use the definition to show that & is bijective. (c) Find & oy. (d) Find the values of x for which 82(x) = 1. - and y(x) = 4 [3] [3] [2] [2]

Q: Use the graphs (see attached) of f and g to find the domain of f + g.

A: Given: Blue line show graph of function f(x). Red line show the graph of function g(x). Domain is…

Q: 5. Function f and g are defined by formulas as shown below. f (x) = x3 and g(x) = x – 1, for all…

A:

Q: tiven the tunction Dn)=(n-5Xhta)(n-3): the coordinates of its P-intercert are, the coordinater of…

A:

Q: (8) 3a. Given the functions f(x) and g(x), find: a) domain b) range c) inverse of the function d)…

A:

Q: Give the domain of the function. Зх — 2 - z = O {(x, y): x and y are real and y + 3x - 2} - {(x, y):…

A:

Q: a) Is the function f(x) = x + odd, even or neither

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: x + 1 (b) Let f(x) = and g(x) = x²+1. x + 2' ii. Determine if f and g are one to one or onto. iii.…

A: According to question given that f(x)=x+1x+2, g(x)=x2+1

Q: c) Is the function f: -2, 2] → -4, 4 with f(x) = x – 2x bijective? %3D

A:

Q: 11. Given the domain and range of a function, state the domain and range of the inverse relation. a)…

A:

Q: Determine if the following relations describe a function. Justify your answer. a) R1 = {(1,8), (2,…

A:

Q: Use the graphs of f and g to evaluate g(f(2)) y (2,4) (4,3) (-2,1) f (2,-2)

A:

Q: 2. Let A:= {1,2,3, 4} =: B and T:= {(a, b) € Ax B | e Z}. (a) Find A x B. (b) Find T (c) Check what…

A: Given: A=1, 2, 3, 4=B and T=a, b∈A×B : a+b+12∈ℤ To find: a) Find A×B b) Find T c) Check what…

Q: Is there a bijective function f: [-1, 1] → [–50, 50]?

A:

Q: Sketch the graph of the relation R= {(x, y)|x² – 2x- 2 < y< 2x – r² + 2}.

A:

Q: How do you show the image of the intersecction of S and T is a subset of the intersection of the…

A: Let function f from A into B. Let S and T are subset of A. To show that fA∩B⊂fA∩fB. Let y∈fA∩B. To…

Q: Original Relation D: Inverse Relation D: R: R:

A: 1)  Original relation : Domain: [-6,9) Range : [-2,10)   Inverse relation : Domain : [-2,10) Range :…

Q: 4. Let D R {-2}, let RR {3}, and let f: DR be defined by a. Prove that f is a bijection. 3x-5 f(x)=…

A:

Q: Which best describes the mapping statements required to transform the function f(x) =…

A:

Q: 5.) Evaluate f(-3) for f(x) = x³ +3x + 17

A: Given  f(x) =x3+3x+17

Q: solve using variation of parameters: x''-6x'+9x=e^(3t)/t^2

A: The order of the differential equation is the highest order derivative present in the equation. The…

Q: (a) Prove the following relation: В (x + 1,у): B(x, y) x +y %3D

A: We have give Beta function relation, we have to show left hand side is equal to right hand side.

Q: elp plssss

A: Statement: Whenever P⇒Q is false then P∧NotQ is true. As it is known that P⇒Q is false only when P…

Q: D. We extend from Q20 to Q by another application of the method of ordered pairs, exactly as we did…

A: To explain: Rational numbers in terms of pair of coordinates using addition operation.

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: could you perhaps elaborate more on transitivity, I can find the relation but I dont know if its…

A: Step 1: Verify reflective and symmetricGiven that   be a relation on the set Reflexive:  For every…

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

A:

Q: Given the function f(x) = x² + 2x – 24, algebraically determine æ-intercept(s) and y-intercept.…

A:

Q: ) Consider the following function: f₁ R → R given by f₁(x): Decide whether this function is…

A:

Q: | Let f(x) = 2x³+3x²-x-5. Determine f[x0, x₁, x2, x3] and ƒ [x0, X₁, X2, X3, X4].

A: