2. Let f:Z→Z be the function given by fAn) =3n+1. a. Is fone-to-one? Briefly explain why. b. Is fonto? Briefly explain why.

Q: On which interval f(x) = -2³ + 3x² - 4 is concave upward? O a. (-1,1) O b. 1 Od. >1

A:

Q: Given the functions f and g where f:R> R, f(x)=-4x² +2x+1 and g:R→ R, g(x)= 2x² – 5. Find fo g. A.…

A:

Q: Consider f : R → R given by f(x) = x². What are the domain, codomain and range of f?

A: Let a function f : A→B thenDomain: set ACodomain: BRange: Values that comes out after putting values…

Q: Sp

A: The question is asking to verify the statement that for all real numbers x and y, the product xy is…

Q: Which relation is not a function? a. N (y) = Vx b. N (y) = ±Vx c. N (y) = -Vx d. N (y) = vx – 1

A: A relation is a function if there is exactly one output for every input.  means for every x value…

Q: -. [T] Sketch a function that has the following properties: O Is a function O D: {xeR[ – 7 3} R:…

A: Topic:- function

Q: Evaluate the function at the given value of the input r6) = -9 p³ – 2 7 + 2, tmd r (-). O1.375-

A: Here we have to put the value of 'p' in the given function to get the solution.

Q: 1. Differentiate the following. Simplify as far as possible. - 3.r)" + (1 – x)² – VF f(x) = V 2+

A: 1)

Q: h. Simplify the function t In 2 N(t)= Noe h, to show that the function can be written in the form…

A:

Q: 3. Let h(x) = (f og)(x). Given f(x) = 3x2 +5 and g(x) = Vx – 3. a. Evaluate h(4). b. Determine fx).

A:

Q: Let (x, y) E R × R. Consider the following functions from R? to R? a((x, y)) = (-x, y) and b((x, y))…

A: Order of the function

Q: Q1: Use third order Lagrange interpolation to Find the value of f(x) when x = 27

A: Given the data

Q: Given a function f: A → B and subsets X,Y C B, prove that f"(XNY) = f(X)nf-(Y).

A: He we will prove the given result.

Q: 口[ A 9. Fill in the table of values. f(x) > V+2 2 f(x) = Vx+2 -3 -2 -1 6. a. 1 b.-2 С. -1 d. 2 e. 3…

A: A

Q: 2. Check the following function f(z) = iz – 3z is analytic or not (Use C.R equations).

A:

Q: Sp

A: The question is asking if the product of two real numbers x and y, represented as 'xy', is equal to…

Q: 3. Let f : A → B. Then 1gf = f and f14 = f. Hint. You may use the fact that fg, for functions f, g,…

A: Let               f1 : X→Y , f2 : X→Y be two functions, then we say that the functions f1 and f2 are…

Q: Let f: R2 R2 be the function given by f(x, y) = (x + y, y). Prove or →>> 8. disprove: f is…

A: Function which is one to one

Q: Let f(r) = 2. 1 + Find f(1/2) 1. Find the domain of f ii.

A: Given data is: fx=11-21+11-x Calculate the value of f12 and the domain of the function.

Q: 6. Let g: X→→ Y and f: Y→ Z be functions. If go f is one-to-one, then f is one-to-one.

A: The given problem is to show for the given functions g and f , if gof is one to one then f is one to…

Q: Let F(x, y) =. Evaluate (31) F dr (1,0,0) O a. 9 + 3e3 8+ 3e3 С. 8— Зе3 O d. 10 – 3e3

A: We will use basic knowledge of vector calculus and integral calculus to answer this question.

Q: V.5. Which of the following functions are injective? Which are surjective? (a) f : Z→ Z given by…

A:

Q: Evaluate the function. 2. Find h(3,6) when h(x,y) = 3x +y J3x+y O A. 9 O B. 10 O C. 3/5 O D. 5/3

A: We have given function  hx,y = 3x+y2 Put x = 3 , y = 6 h3,6 = 3×3+62 h3,6 = 9+36 h3,6 = 45 h3,6 = 35

Q: Using the Envelope theorem, compute the slope of the following function y=-x² +9x

A:

Q: H.W: Determine which the following functions are differentiable. a) f(z) ix ze.e 6) f(Z) =

A: Let us consider the complex function f(z)=u+iv then the function is differentiable if and only if…

Q: . Consider the function f: Z x Z → Z × Z defined as f(n, m) = (n +m, 3n + 4m). (d) Find the inverse…

A: I have find two equation in variables m & n and solved them