8. (p.241, #4) The function f: R → (0, 0) defined by f (x) = e**+1 is bijective. Find its inverse.

Q: Find the inverse of the following functions (a) f :R +R, f(x) = 2, (b) f:R- {}→R - {}, f(x) = - 3-2z…

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Q: Find the Green's function G" + k²G = 8(x − s), Gʻ(0, s) = 0, G′(0,π) = 0 -

A: To find the Green's function G(x,s) for the given differential equation G′′+k2G=δ(x−s), subject to…

Q: Determine whether the given set of functions is linearly independent on the interval (-00, 00). fi…

A: We have to determine that whether the following set of functions are linearly independent or…

Q: Consider the functions f(t) = e' and g(t) -81 defined on 0 st<o. %3D = e (a) (f* g)(t) can be…

A: Consider the functions, f(t) = et and g(t) = e-8t

Q: The Domain of f (x) = V1 – x is 1. [-1, 0) 2. (-∞, 1] 3. (-0, 1) 4. [1, c0)

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Q: Derive the autocorrelation function of: x₁ = $xt-1 + εt + 0€t-1 assuming that p < 1, and E(?) = 0²,…

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Q: Which of the following is the inverse of the functionf : [0, ∞) → [3, 0), f(x) = 2.x² + 3? Select…

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Q: Suppose that y is a function of u, u is a function of x, and u = -1 when x = 2. If du/dx|x=2 = 3 and…

A: Solution

Q: Show that the function f(x) =r³ – x² + 1, x > has an inverse. 3 If g is the inverse of f, find…

A: Part a:   In part a function f(x) is given and show that the function has an inverse for x&gt;2/3.…

Q: [59] Evaluate F.dr where F(x.y)3y'i+(x-4)j and C is the portion of y=(x-1) from .x-0 to r-3.

A: Please see the explanation below

Q: The function y = (x- 1)(x-2)(x - 3) is negative on the interval(s) %3D O a) xe (-0, 1) and x e (2,…

A: We have y=x-1x-2x-3 First, we find the critical points by letting y=0: y=0⇒x-1x-2x-3=0⇒x-1=0, x-2=0,…

Q: The inverse of the function f(x) = +4 is f() = O 42(x- 4) O 6(x – 4) O 6(x – 8) O 30(x-4) O 12(r 4)

A: We have to find inverse of given function.

Q: Let f(x) = 4x- 1, h(x)= -x+1. %D Find (f o h)(3). (f o h){3} =] %3D

A: Composite function  foh (x) is given by  foh(x) = f(h(x))

Q: 3. Consider the function Prove that f'(0) = 0. & f(x) = if r EQ if x & Q.

A: Introduction: A differentiable characteristic of 1 actual variable is one whose spinoff takes place…

Q: If I attend a movie marathon of 3 movies and their respective run times are 147, 121 minutes and 92…

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Q: Let f(x) = = a) 9x +4 following. Simplify if possible. f(x) = f(a) a - X = . Evaluate the 4 A' for x…

A: The given function fx=x9x+4. We have to simplify the expression fx-fax-a and find the value of A.

Q: By listing the elements as ordered pairs, define a relation on the set A = {e, 2, 7, ♡} which is:…

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Q: 6. Define f(x) = x³ – Ax2 – 12x where A> 0 is a constant. (a) Show that f is one-to-one on S =…

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Q: 3. Find f. (g) f'(x) = 2x – e

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Q: 5- Verify that the given function u is harmonic in an appropriate domain D. Find v(x,y), the…

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Q: 1 f (x) = x+÷, then the set of values for which f increases is | Select one: |(-x, –1]U[1,) а.…

A: The function increases when the function has positive slope. The slope can be calculated by…

Q: (x +1)4 – y² Let f(x, y) = { (x + 1)4 + y? - if (x, y) # (–1,0) -1 if (x, y) = (-1,0) a. Show that f…

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Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.