Let f: Z → Z be defined by f(x) = x² + 1, and let C = {1,2,3}. Find f(C), f-¹(C), f-¯¹(ƒ(C)) and f(f−¹(C)).

Q: Let f(x, y) = 125-3x²-2y2² Evaluate f(0, 3)

A: f(x,y)=sqrt(125-3x2-2y2)Find f(0,3)

Q: Find all analytic functions f = u + iv with u(x, y) = x² - y². Simplify the expression f(2) as much…

A:

Q: 1. Find the most general antiderivative or indefinite integral for the function. (Ilint: Using a…

A: to find integration.

Q: 3. (b) Consider the function f(x, y) = a(x² + y²) + xy + 1 for some real number a. Find Vf. Find fxx…

A:

Q: Find the linear function f(x) passing through (6,8) and (8,10) Enter answer in form…

A: Explanation of the answer is as follows

Q: z) = (x2 + then (a + E

A:

Q: Find f"(x) for the function: f(x) = x – 1. -2(x– 1)-2 2(x – 1)2 O 2(x – 1)-3 -2(x– 1)

A: Derivative of a function

Q: Let T:P, →02 be the function defined by the formula T (p(x))=(p(0),p(1)). Then T- (3,5)= (а) 3—2х…

A: Here given T:P1→R2  be a function defind by the formula T(p(x))=(p(0),p(1)). We have to find…

Q: What does is mean for two functions f(x) and g(x) to be orthogonal

A:

Q: Let f(x, y) = 3x² + 4y? – axy. (a) Find the values of a such that the graph of f increases when…

A:

Q: Let f(x) = 4x+3. Determine (fofo f)(x).

A: Given,          The function is fx=4x+3 .

Q: 2 Suppose y is a function of x such that y * and y(4) = -3. Find y. |

A: The differential equation is given by y' = 2x                                   .......(1) Initial…

Q: Let n be a positive integer. Define the function fn(z) by dzn (2²+2x+2)". Find the value of fn(-1 +…

A: Solution:Given: Let be a positive integer. the function is defined bywe have to find the value of

Q: Let f(x, y) = e"r³ Evaluate f(3, 0)

A: The function of two variables  x and y will be of the form,   The function value of this kind of…

Q: Let f(x)= -x-1, h(x) = -x + 5. Find (h of)(2). (hof)(2) =

A: The answer is given below: Topic: Composite Function

Q: Let F = (2xz+y², 2xy, x²+1), if Vf= F, find f(1, 1, 1) – f(0, 0, 0)

A: Given vector funtion and

Q: Find the values of x for which the gradient of the tangent to the graph of y=f(x) is equal to the…

A: We have to find the values of x for which the gradient of the tangent to the graph of y=f(x) is…