1. f is an onto function from R³ to R3 2. f is a function from R3 to R3 3. f is a one-to-one function from R' to R 3 A. For every x ER’, there is a y E R' such that f(x) = y. B. For every y E R’, there is a x E R’ such that f(x) = y. C. For every y E R’, there is at most one x ER’ such that f(x) = y. D. For every y E R’, there is a unique x E R’ such that f(x) = y. 3 3 3 %3D

Q: 18. The graph of the function f shown in the figure to the right has a vertical tangent at the point…

A: A graph of the function is given.The aim is to find the points in the interval  for which  is not…

Q: 1. For each of the following relations, indicate whether it is a function. If it is a function, give…

A: As per our guidelines we are supposed to answer only first question. Please repost rest question…

Q: Consider the function g(x) = (x - 1)e(1-2) +1, TER. Which of the following intervals makes the…

A:

Q: Which of the following functions are monotonic on their natural domains? Check all that apply. O y =…

A: We have to find the functions which are monotonic on their natural domains.

Q: Let X={1, 2, …, 16} and define function f(x)=rx for all x€X where rx is the remainder when 3x is…

A:

Q: For which values of a ∈ R is the function f(x + iy) = (a2x - axy) + i(- ax2/2 + ay), an entire…

A:

Q: Sketch the graph of a function f that is defined over all real numbers and that is decreasing on the…

A: Given: f(x) is decreasing on the interval -2,3. f(x) is concave down on the interval -2,2 f(x) is…

Q: 1. Given a function f : A → B. Define the relation f from P(A) to P(B) by f= {(X,Y) Ɛ P(A) × P(B)|Y…

A:

Q: a. Let X = {2, 4, 6} and Y = {a, b, c, d'}. Define g : X→ Y by the following arrow diagram. X 2 4 bo…

A:

Q: 19 For X = {1, 2, 3} and Y= {a, b, c), functions f. X - Y and g: Y-X are defined as follows: 1. NT 2…

A:

Q: 6.3 Let g: R → R be a real-valued function defined by g(x) = x² + 2x - 1. Let A = (-2,3], and B =…

A:

Q: 1. Let f(x) = r3 – 12r. This function is: • Increasing on (-0, -2) and on (2, 00) • Decreasing on…

A: Solve by finding minima and maxima

Q: 1. Let f be the function defined by f(x)=/x+ 2 . Prove that f is one-to-one .

A: Dear student as per our rule in one session we can only solve the first three subparts of one…

Q: Consider the function f whose graph is drawn below. For which values of x is the function…

A:

Q: Let C be the contour (blue) given in the figure below and let f(z) be any function with If(2)| <v2.…

A:

Q: 6. Let S = {-1,0, 2, 4, 7}. Find f(S) (image of S under f) where f is from R to R for (a) f(a) = 1…

A: The

Q: The graph shown is the 1st derivative of function where its domain is R फ़ी An interval where the…

A: topic - strictly  decreasing  interval of function

Q: 4. Let function f: R → R and function g: R → R be two functions for which f(g(x)) = x and g(f(x)) =…

A: We have to prove given statement.

Q: Determine which of the following functions are one-to-one. OA. f: R² → R² defined by f(x, y) = (x +…

A: The given functions,A) defined by .B) defined by .C) defined by .D) defined by .E) defined by…

Q: Determine which of the following functions are one-to-one. OA. f: R² R2 defined by f(x, y)= (x + y,…

A: Note - According to answering guidelines I will solve the first three parts. Pls post the other…

Q: The table contains some input-output pairs for the functions f and g. æ| f(x) | g(x) 2 2 9 6 9 3 9.…

A: To evaluate the given expression with the given table values.

Q: Which of the following functions on R is sublinear? a). s1(x) = # x if x ≥ 0 0 if x 0

A: Definition: Let X be a vector space. A function p: X→ℝ is said to be a sublinear function, if it…

Q: 19. The function f is defined by f:x 1+x*ER + f is injective. B f is surjective. C f is neither…

A: Please see the explanation below.

Q: d. For each of the following, state whether the functions f: R → R, x → f(x) are injective,…

A: Given functions: fx=3x+2 fx=3x3-7x+3 fx=x6 fx=sinx fx=0.01x fx=4 We have to check whether the…

Q: Inverse Functions beduined Let f: R→ R be defined by f(x) = 3x +2. Show that f is bijective and find…

A:

Q: 2. What is the count of a. all possible functions F:{0,135 (0, 13º ? b. All possible functions…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: 7. For each of the following, give an example of functions f: A → B and g: B C that satisfy the…

A:

Q: Find the domain of the given function f(x,y) = 3x² - 4y².

A: