Find the domain of the function. if x < 2 f(x) : х x2 if x > 6 O(-0, 0) U (0, 2] U (6, 0) O(-0, 0) U [2, ∞) O(-∞, 2) U [6, ∞) O(2, 6] O(-0, 0) U (0, 2) U [6, ∞) Evaluate f(-6) and f(8). f(-6) f(8)

Q: Find the absolute maximum and absolute minimum values of f on the given interval. (a) f(x) = 2x³ —…

A: The given functions, a) f(x)=2x3-3x2-12x+1, -2,3b) gθ=θ+cotθ2, π4,7π4

Q: х- 3, x2

A: Given:      Let fx=x-34-x2x2-3x&lt;-2-2≤x≤2x&gt;2              gx=x2-x+1   For x=-12        fx=x-3 ,…

Q: A. Prove that the function is discontinuous at the number a. Determine whether the discontinuity is…

A: 1. The given function is a rational function. For a rational function to be defined it is a must…

Q: B) Test the functions continuity at the given poihts: (x²-x-6 1) f(x) 3D x * 3 ,at x 3, x 5 X-3 x =…

A: f(x)=x2-x-6x-3x≠35x=3

Q: The function f(x) is continuous on the interval [-1,3]. The table below gives some of its values.…

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Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

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Q: Find the the domain of the function f(z) = O {x|x / 10} O{x|x + T} O x x 10 and x-7} O x 1 x -10 and…

A: Find the domain of the function

Q: Find the critical numbers for the function f(x) = x' - 12x. Select one or more: O a. x = 2,4 O b. x…

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Q: constant k is the functionf defined by if x +0 f(x) = V5- x - V5+x k if x = 0 continuous at x = 0?…

A: On putting limit x tends to 0 when condition of not equality it becomes 0/0 form . So by…

Q: Function f is defined by f(x) = 2x – 7 and g is defined by g(x) = 5*. a. Find f(3),f(2),f(1),f(0),…

A: a. consider the given function, fx=2x-7 substitute x=3 in the function to find the value of f3,…

Q: 1. Let f be a function from A to B, and X, Y C B. Show that f-(XnY) = f-'(X)nf-(Y).

A:

Q: f (x) + 5 f(x) – 3 g(x) (4) Let f(x) = mx+b, where m and b are constants and m 6= 0. Prove that the…

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Q: 1 The residues of a function f(z) are (:-4)(=+1)

A: Introduction :

Q: 19 If f(x) be continuous function for all real values of x and satisfies; x + {f(x) – 2 }x + 23 - 3…

A: Introduction :

Q: Determine whether there exists a function f : [0, 2] → R or none such that f(0) = -1, f(2)= 4 and…

A: In this question, we need to determine whether there exists any function for the given conditions.

Q: x² + 2 if x < 0 b) f(x) = ax + b if 0sx<1, (3 + 2x- x2 if x 21 determine a and b, such that the…

A:

Q: The critical points of the function f(a) = 16z2 – 2z* occur at O * =0, z =±1.00 O z =0,2 =±8.00 O *…

A: To find critical point, put f'(x) = 0.

Q: The function 3 y = -x³ (2x – 3)(4x + 3)° is negative on the intervals ) a) x E (-∞, –) and x 4 X 3 E…

A: The given function is: y=-x3(2x-3)(4x+3)3

Q: (c) The function f(x) is defined in the interval [-1,6] by 3-x, -1<x<2 f(x) ={ x -a, 2<x<b…

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Q: 1. Determine whether Rolle's Theorem applies to the function on the given interval. If it applies,…

A: a. Given function

Q: 2:46 Find the value of the constants a and b that makes the function continuous. Define x-1 : x

A: Consider the given piecewise function and the condition for the function f(x) to be continuous.

Q: 17) Let f(x) : Find a %3D X - 9 function y = g(x) so that (f •g)(x) = x. %3D

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Q: The function f is constant on I if ________.

A: To determine when the function f is constant on I.

Q: Consider the function= f(x.y) =-X"-y² + xy3 + 5 and classify Find the critical points of f these…

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Q: Find and classify the critical points of the function f(x,y)=3y^2 −12x^2 +12xy^2 +16x^3

A: Given function: fx,y=3y2-12x2+12xy2+16x3 Formulas used: ddxxn=nxn-1ddxconstant=0 To classify the…

Q: 18. A function f: R R is defined by f: x → 3x Determine whether or not f is 2x+1 surjective. x3

A: The objective is to determine whether the function is surjective or not.

Q: An even function f(x) for all values of x and x holds a. f(x) = f(-x) b. f(x) = -f(x) c. f(x) =…

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Q: f(x)= -2x+3 if x>-1 it メニー」 3+ ax2 if xc-1 if xa-I Is the fanciono continuous at x>-1?

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Q: 1+x2+y2 Determine the set of points at which the function F(x, y) = is continuous. 1-x2-y2

A: In this we have to check Discontinuity of equation.

Q: The question is in the picture below.

A: As given the f(x) is continuous on R so it will continuous at x=2 and x=1 , then limit will exists…

Q: (рx* + x — q, 2х + q, x< 2 2 < x < 5 i: x 2 5 For what values of p and q the function f (x) %3D 2рх…

A: function is continuous at every xlimx→2-f(x) = limx→2+f(x)p(2)2+(2)-q = 2(2)+q4p+2-q = 4+q⇒4p-2q-2=0…

Q: Consider the function f(x) = 3x + 3x. For this function there are four important intervals: (- 00,…

A: Function problem

Q: Find functions f and g so that h(x) = (f o g)(x). h(x)-2 -7 f(x) = 1/x-, g(x) =x - 7 f(x) = 1/x²,…

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Q: 1) Determine the value of c such that the function is continuous Vx E R. Show and explain in…

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Q: 3. Determine the values of a and b if the given function f(x) is continuous. 1 ,x 2

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Q: (a) Let f: R 11 k=1 R be a function given by f(x1,x2,...,xn) = x²₁x²...x2, where 1. Show that the…

A: As per our guidelines we are supposed to answer only one question. Here first question answered.

Q: 17. The function f(x) = 2 + 2x2 - x* is increasing on: %3D A) (-00, -1) only. B) (-1,0) and (1, c0).…

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Q: Find the values of x for which the function is continuous. 9 f(x) = Z+4 x2 +4 O x>0 O x > -2 O x<-2…

A: Now the domain of f(x) is the set of all values of x for which denominator is non-zero. That is,

Q: The graph of y = f(x) is graphed below. What is the end behavior of f (x)? 500 400 30 200 100 10 -8…

A: Analysing the graph of f(x) when the value of x is tending to infinity and-infinity

Q: True or False A function f is decreasing on an interval I if, for any choice of x1 and x2 in I, with…

A: Given: True or False A function f is decreasing on an interval I if, for any choice of x1 and x2 in…

Q: (b) The function f is defined by 5 X7 5 Determine the values of A and B if f is continuous at x=--…

A: the given function f is defined by: fx=Ax2-6,       x≤-54Bx+A,          -54&lt;x&lt;725,…

Q: IV. Verify Rolle's theorem for the function: f(x) = x2 – 5x + 6 on [2,3] а.

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Q: Find the domain of the function f(x) = x² – 1. In interval form, the domain of f is (-∞, 0). x + 1…

A: To find the domain of the below functions,  a) f(x) = x2 - 1 b) f(x) = (x + 1)/(2 - x)

Q: 1- describe all functions y=f(x) which are defined for all x∈R and satisfy the equation f(x)=1/f(x)…

A: We need to find all functions y=f(x) which are defined for all x∈R and satisfy the equation…

Q: E. Discuss the continuity of the function g(x) = on the interval (0,2] and [-1,3]. x2-4

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Q: 3. Find constants A and B that make the function continuous and differentiable for all x. Ax x > 1…

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Q: D. Discuss the continuity of the function on the closed interval. Function Interval 1. g(x) V49 [-7,…

A: Note: We are entitled to solve only one question at a time. Given: gx=49-x2 To Discuss: Continuity…