11 f(x) dx = 31. 10 Then f(x) dx 3

Q: 5. If f(x)=-3x+5 a) Find f-¹(x). b) Use function composition to prove that they are inverse…

A: a) finding the inverse of f(x)

Q: Is there a function that is both even and odd?

A: Yes, f(x)=0 is both even and odd.

Q: Graph the piecewise function defined by

A:

Q: The third interval of the following function xe* - 1, which between 0 and 1 is [2,3]. True False

A:

Q: A function and its graph are given. Fx) = + 4x - 20x - 20 250 200 150 100 50 -10 -5 - 50 (a) From…

A:

Q: A fixed point of a function f is a number c in its domain that satisfies f(c).  In other words, the…

A: Given: A fixed point of a function f is a number c in its domain that satisfies f(c).

Q: Consider two sets, A and B, such that A = {1, 2, 3, 4} and B = {3, 4, 5, 6}. Let f be a function…

A: A function is a rule that assigns each element in one set (called the domain) to exactly one element…

Q: 5. Ôx (@) = ¢x (- w), if X is symmetric function.

A:

Q: Let f(x) = (x + 5)?. Find a domain on which f is one-to-one and non-decreasing. Find the inverse of…

A:

Q: y = C¡e e-2= + Cze³* + C2e%

A:

Q: 2. Let a, b be real numbers for which b > a. Let functions f,9,h be defined on a domain [a, b] in…

A: Solution is here

Q: уто ņx=-5 O SONGS & + 10 9 7 6 5 4 012345 -10-9-8-7 -6 -5 -4 -3 -2 -10 -2 -4 1) lim f(x) = x-(-4)…

A: Sol:- We have to explain what is telling by limits and the points for which f(x) is not…

Q: Let X=[-1,1] and Y=[0,1], and define the function f:X-->Y by f(x)=x^2. Which of the following is NOT…

A:

Q: 1.Solve the following polynomial equations.  a)  2X3+1=x2+2X

A:

Q: Which of the following is the graph of f(x)= (x-2)^3 A,B,C,D, or E??

A: Given: function is fx=x-23. To be find: which one is the correct graph of the given function.…

Q: f(x) = 1- (x - 1), xs2 lx-2, x > 2 y y 10 10 5 -10 -5 10 - 10 -5 10 -5 -5 - 10 -10 y y 10 10 5 - 10…

A: Topic - functions and their graph

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.