5. Function f and g are defined by formulas as shown below. f (x) = x3 and g(x) = x – 1, for all real number x. i) Find gof and fog. ii) Determine whether gof equals f og.

Q: on satisfying f'(x) the function sat

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Q: 2. If p and q are positive integers, f is a function defined for positive numbers and attains only…

A: Introduction :

Q: Prove that f(x) = (x – 1)2 + (x + 1)? is an even function. A function k(x) is an even function if…

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Q: (b) Given the set S = [-1,1] and the function g: S→ R defined by g(x) = that g is one-to-one, and…

A: g is one to one because  For every x there is a different image in g(x) if x= -1 then it's image is…

Q: 8. Find all the points in the interval [1,5] for f(x) = -x² + 6x – 6 such that the function verifies…

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Q: (a)Verify Rolle's Theorem for f (x)=x - 16x+10 over the interval [0,4].

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Q: Find a point c satisfying the conclusion of the MVT for the function y(x) = 8e* on the interval…

A: Let the given function is  y(x)=8ex  on the interval [0, 9]

Q: 5.16] Use the function f (x) = xe¯ ¯x² to find fave on [0,4] %3D

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Q: 2. Determine whether the function y= -x5 + x3 – 1 is even, odd, or neither. Justify your ans wer.

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Q: (b)(is) Verify that the function satisfies the hypotheses of Rolle's Theorem on the given interval.…

A: Explanation of the answer is as follows

Q: If f(x) = prove that f (x) is an even fun %3D et-1 2

A: Introduction :

Q: 3. If G(x) = tan x, find G(t/6), G(x - x/2), G(-x) and express G(2x) as function of G(x).

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 2. Consider a ball thrown in the air (f) defined by the formula f(x) = (3 + x)^2 whose domain is the…

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Q: 5. Verify the three conditions of the hypothesis of Rolle's theorem are satisfied by the given…

A: 5)  As per our norms we have to write one question at a time kindly repost remaining questions

Q: 1 1. -to prove that x+y|# | x|+ | y| for all real numbers d) Use x = and y = %3D x and y.

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Q: B- Obtain PDE by eliminating the arbitrary functions from the following; 2- Ix + my + nz = Ø (x2 +…

A: We have to obtain PDE by eliminating the arbitrary function from  lx+my+nz = ϕx2+y2+z2.

Q: Determine whether Rolle's Theorem can be applied to 22 –1 f (x) on the closed interval –1, 1. If…

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Q: 2. Let f(x) = e" + for x E [0,3]. Determine the length of the graph of f. 4e

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Q: 9. Use the given graph of f (x) x2 to find a number 8 such that %3D if |x – 1| < 8 then |x2 – 1| <;…

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Q: 12. Give the x-coordinates of all points where f is not differentiable. Iff is differentiable…

A: Given: The graph of the function, f as shown below:

Q: 3. Determine whether the functions e2a and xe2 by calculating Wronskian.

A: Let f(x) = e2x and g(x) = xe2x Then,  f'(x) = 2e2x ,and g'(x) = e2x+2xe2x (by using chain-rule of…

Q: 11. What property must f(x) have in order for f'(x) to exist?

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Q: Let f(x) = Vx +7 and g(x) = x +3 a) Find (2) (2) show work. b) Give the domain of the function (-)…

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Q: Suppose that the function h is defined on the interval-2, 2) as follows. -2 if-2<x<-1 -1 if-1<x<0 h…

A: Given:     To determine: h(-2), h(-1.5), h(1)

Q: The domain of the function f(x)= tanh( x - 10) is Select one: O[-10, 10] O(0, ) None OR-{10} O [ 10,…

A: Set of values of x for which function is well defined is called domain of the function

Q: If we apply Rolle's Theorem to the function f(x) = 2x- 16x 6 on the interval [2, 6|, how many values…

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Q: 2 - Given that f(x) = (x)6 pue 2x + 1 find (gof)(x) and determine the domain of (go f)(x).

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Q: Verify that the function f(x) = x3 – 2x² – 4x + 2 satisfies the hypotheses of Rolle's Theorem on the…

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Q: 2. If p and q are positive integers, f is a function defined for positive numbers and attains only…

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Q: 2. Determine whether Rolle's Theorem can be applied tof on the closed interval [a,b]. If Rolle's…

A: Here rolles theorem is applicable.

Q: 2) Use Rolle's Theorem on f(x) = 2x3 - 6x² - 2x + 6 to find all numbers c in the interval (1, 3) for…

A: Here is the solution:

Q: The function g is defined by the following rule. -()- IN g (x): %3D 6. Find g(x) for each x-value in…

A: Topic - functions

Q: 1 and the domain for g(x) is a s as x-> inf, f(x) -> inf and the

A: Domain of a function: All the possible values of x that makes the function f(x) valid or the values…

Q: 4. Suppose that f and g are continuous on the closed interval [a,b] and dif- ferentiable on the open…

A: That's easy, you just need to use Lagranges mean value theorem and given conditions and then the…

Q: A periodic function f, is defined on R , the set of real numbers by 34. 0<x<3, 3 <x5 5, f(x) = {2x –…

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Q: Which of the following is the domain set of the function f(x.y)= arccos(x² + y² - 3)+In(x² +y² -3) ?

A: In this question, we evaluate the domain of multivariable function and in second part we check the…

Q: a) Verify Rolle's Theorem for ƒ(x)= 2.x' – 8.x + 4 over the interval [0,2].

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Q: 5. If f(x)= kx³ + x² – kx+2, find k such that the graph of f contains the point (2, 12).

A: Given

Q: Let g(x) = x². Which of the following outputs of g is not guaranteed by the Intermediate Value…

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Q: If we apply Rolle's Theorem to the function f(x) = 2x² - 8x - 1 on the interval [0, 4], how many…

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Q: 5. Let f, and f, be the function from R to R such that f,(x) = x²+2x+3 and f,(x) = x-x. What are the…

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Q: If g (x) = 1 - x, defined at 0 ≤ x ≤ 1, graph its extension on the interval [-1, 1].

A: extension of the function

Q: Show that a function f(x) = ∑ ∞n=2 (1/x-nπ + 1/nπ) is well defined on [0, π]. That is, prove the…

A: Given function,

Q: I have no idea how to approach this question.  Any insight would be greatly appreciated.

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Q: 2. If f(2) = e*, describe the images under f(2) of horizontal and vertical lines, i.e. what are the…

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Q: Find a point c satisfying the conclusion of the MVT for the function y(x) = 2e* on the interval…

A: Solution: The objective is to find a point c

Q: 1 -Find all the points where f(2)is analytic. 2+3 Let /(2) =

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Q: 11. The function f: R – {-2} → R is defined by f(x) : x+2 Determine f'(1) and verify your answer…

A: First we have to find  f'(1) and have to verify it by € _ delta definition.

Q: 3. Prove that the function f: R – {3} → R - {1} defined by f(x) = , is one-to-one correspondence.

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