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As I understand the question: yes, f(x) can be a function even if f(x) is not defined for all x. For example, f(x) = x/x is a function that is equal to 1 everywhere but at x=0, where it is undefined.
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What is the relationship between roots and zeros and factors?
Given a function f, of a variable x, the roots of the equation are values of x for which f(x) = 0.If the function, f, happens to be a polynomial function, and r is a root of f(x) then (x - r) is a factor of f(x).
How do you prove decreasing function theorem?
this is the increasing function theorem, hope it helps "If F'(x) >= 0 , and all x's are and element of [a,b], Then F is increasing on [a,b]" use Mean Value Theorem (M.V.T) Let F'(x)>=0 on some interval Let x1< x2 (points from that interval) by M.V.T there is a point C which is an element of [x1,x2] such that F(x2)-F(x1) / X2- X1 = F'(C) this implies: F(x2)-F(x1) = F'(C) X [x2-x1] F'(C)>=0 [x2-x1]>0 therefore: F(x2)>=F(x1) Therefore: F is increasing on that interval.
Describe how the Factor Theorem can be used to determine whether x plus 1 is a factor of x3-2x2-8x-5?
The factor theorem states that for any polynomial function f(x), if f(a) = 0, then (x-a) is a factor of f(x). Let f(x) = x3-2x2-8x-5. If (x+1) is a factor, then f(-1) = 0. (x+1 = x - (-1)) Input x = -1 into f: (-1)3-2(-1)2-8(-1)-5 f(-1) = -1 -2 + 8 - 5 f(-1) = 0. Since f(-1) = 0, (x+1) is a factor of x3-2x2-8x-5. Q.E.D.
How can you use the zeros of a function to find the maximum or minimum value of the function?
You cannot. The function f(x) = x2 + 1 has no real zeros. But it does have a minimum.
Is the function n divided by 3 one to one and onto?
This depends on how you define your domain and codomain. f(n)=n/3 is one to one and onto when f is from R to R, but if we define f: X --> Y, where X = [0,3] and Y = [0,3], then f maps [0,3] to [0,1], so f is not onto in this case.
What is the composition of an even and an odd function?
For an even function, f(-x) = f(x) for all x. For an odd function, f(-x) = -f(x) for all x.
What is even and odd wave function?
A basic wave function is a sine or cosine function whose amplitude may have a value other than 1. The cosine function is an even function because it is symmetrical about the y-axis. That is, f(-x) = f(x) for all x. The sine function is an odd function because it is antisymmetrical about the y-axis. That is, f(-x) = -f(x) for all x.
Which statement best describes how to determine whether f(x) 9 and 4x2 is an odd function?
It is difficult to tell what function you have in the question because the browser used by this site is hopelessly inadequate for mathematical notation.However,f(x) is an odd function of x if and only if f(-x) = -f(x) for all x.Common examples are f(x) = x^k where k is any odd integer, f(x) = sin(x).
f(x)= â x2fâ˛â˛(x)=?
The function given is (f(x) = -x^2). The second derivative of a function, denoted as (fâ'(x)), measures the concavity of the function. For the function (f(x) = -x^2), the first derivative (fâ(x)) is (-2x). Taking the derivative of (fâ(x)) gives us the second derivative (fââ(x)), which is (-2). So, (fâ'(x) = -2). This indicates that the function (f(x) = -x^2) is concave down for all (x), because the second derivative is negative.
What is a function that is symmetric with respect to the y-axis?
A function that is symmetric with respect to the y-axis is an even function.A function f is an even function if f(-x) = f(x) for all x in the domain of f. that is that the right side of the equation does not change if x is replaced with -x. For example,f(x) = x^2f(-x) = (-x)^2 = x^2
What is the solution for function of function of x equals function of x?
f(f(x)) = f(x). Only if f is 1-1 then we have a solution f(x)=x.
How do you determine if a function is even?
A function f(x) is Even, if f(x) = f(-x) Odd, if f(x) = -f(-x)
How do you identify the roots of a function algebra 1?
If the function of the variable x, is f(x) then the roots are all the values of x (in the relevant domain) for which f(x) = 0.
Determine whether a function is even odd or neither?
If f(-x) = f(x) for all x then x is even. Example f(x) = cos(x). If f(-x) = -f(x) for all x then x is odd. Example f(x) = sin(x). In all other cases, f(x) is neither.
Does h of x mean the same thing as Function of x also known as f of x?
Yes, h(x) is simply a function h --> x, like f(x) is a function f --> x. The different letters are used to illustrate the fact that the two functions need not be the same.
How can you determine whether a function is even odd or neither?
Looking at the graph of the function can give you a good idea. However, to actually prove that it is even or odd may be more complicated. Using the definition of "even" and "odd", for an even function, you have to prove that f(x) = f(-x) for all values of "x"; and for an odd function, you have to prove that f(x) = -f(-x) for all values of "x".
Is it true or false that the limit of a function f x at x equals 2 is always the value of the function at x equals 2 that is f 2?
False. It is true for a function that is continuous at x=2, but it is not generally true for all functions. For a counterexample, consider the function f(x), such that: f(x)=x for x not equal to 2 f(x)=0 for x=2 The limit of this function as x approaches 2 is 2 (since we can make f(x) as close to 2 as we want as x gets closer to 2), but f(2) does not equal the limit of f(x) as x approaches 2.
