T: HH be a bounded operator with closed range. Can we say that for each x H, there exist que elements x ER(T).x₂ € R(T)-such that x= x₁ + x₂ and (Tx,x)=(Tx₁.x₂). (Proof or unter-example with details).

Q: Let f(x) = (x-9)7 – 8, determine f¯¹(x). - ƒ¯¹(x) =

A: To find the inverse of the function f(x) = (x - 9)7 - 8, we need to express x in terms of y, where y…

Q: 1)Given the relation f (x) = {(-3,0) (2,5) (-1,7) (-3,8)} state whether f(x) is a function or not.…

A:

Q: 12 - y = | 4-x | Which of the following is the value set of the function? A) (-∞, 0) B) (-∞, ∞)…

A:

Q: Indicate which of the following point(s) are on the graph of this function. You must indicate ALL…

A: Here we need to put the value of x in the function as per it definition then we check wether it…

Q: e*+1 Differentiate the function f(x)= In -3x +1 -3e A) 4e** +1 +1 3e B) e +1 +1 3e C) 3x 1. D) E) +1

A: Topic: differentiation

Q: V2(x+3): xEQ x² + 3x: x €Q Let f: R R be defined as f(x)=. The set of all points at which f is…

A:

Q: 4. A function f may have the property that, for all numbers a and b in the domain of f, f(a) + f(b)…

A: GIVEN : f(a) + f(b) = f(a + b)

Q: Give an interpretation that satisfy the indicated FOL sentence For all x (F(x) or not G(x))…

A: The first-order logic (FOL) sentence given is "For all x (F(x) or not G(x))".This sentence can be…

Q: Let a = (-2,3, –4)" , y = (3,-2, -5)". (a) Find ||a||1. (b) Find ||a||2- (c) Find ||y||o-

A: Given Information -  x = -23-4  and  y = 3-2-5We have to find the following - (a) x1(b) x2(c) y∞…

Q: x=[-5,-4,-3,-2,-1,0,1,2,3,4,5], A= [0.45    0.61    0.75    0.88    0.96   1    0.96    0.88    0.75…

A: Given: x=[-5,-4,-3,-2,-1,0,1,2,3,4,5], A= [0.45    0.61    0.75    0.88    0.96   1    0.96    0.88…

Q: 3. There are two conditions that must be met in order for a function to be continuous, explain those…

A: See a function is continuous at a point a when these two conditions are satisfied,i) ii) Note that…

Q: 1. State the domain and range of f(x) = /9(x - 4) + 2 D:[2,00) A. D:[4,00) В. D:[4,00) D:[2,00) D.…

A:

Q: 4. Select all the true statements about the end behavior of the function f(x) = -x*-5x .4 + 5x +3.…

A: Given :

Q: What is the domain of the relation x(x-3) ? {(X,y): y = (x+4)(x-7)). ) {x: x = R, x -4, x > 7} ) {x:…

A: Domain of function f(x) is the set of value of x for which f(x) is defined.

Q: Determine the end (long run) behavior for the function below: f(x) = x - 3x³ + x – 1 Select the…

A:

Q: f(x) = - 4x+5 if -1<x<2 3x-8 if 2≤x≤4 The domain of the piecewise defined function fis [-1,2]U[2,4]

A: Given a piece wise function

Q: If f (x) = x² - x and g(x)=√x-2, what is (fog)(x) ? Simplify your answer. x²-x-2 /x² - 2 2-x-2 O…

A:

Q: If A and B are operators, and Q is a function then, АВО-ВАQ is Must always be true May be right or…

A: Consider the following. A=ddxB=Q=xABQ=ddxxABQ=ddxxABQ=12xBAQ=ddxxBAQ=ddxxBAQ=1=1⇒ABQ≠BAQ

Q: Use calculus to find the absolute maximum value and the absolute minimum value, if any, of the…

A: Topic:- calculus

Q: 1) Which set of values for x should be tested to determine the possible zeros of the function f (x)…

A: We need to find possible x values that needs to be checked where function is zero.   NOTE - As per…

Q: Funchion figandx are follows f(2)- H-14 +421, g12)= Tio-22 , hca)- 5+x find, Find %3D 2. g (4) = h…

A:

Q: 4. please help!'   Calculate the domain of the function:

A: Step 1:

Q: 6. Let f(x) = x − 1 and g(x) = (x + 2)², find the following: a) Domain of f(x) b) Range of f(x) c)…

A: "Since you have posted a question with multiple subparts, we will solve the first three subparts for…

Q: EXercises - I5 § conlinumus ad.xaz X72 X=2 Xくス -2X

A: Since you have posted multiple question in this question thus I have solved first question as per…