Drag a function or an interval into each box to correctly complete the statement. When the domain of the non-imnveritie function f (x) = (x+1) -3 [-1, 00). ,the inverse of the function is and the domain of the inverse function is f1 (x) = Vx- 3+1 [-1, 0) [3, 0) f (x) = Va+3 - 1[-3, 0)

Q: Prove that the function given by f(x) =x3-3x2+3x-100 is increasing in R

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

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Q: Verify the Rolle's Theorem for the function (x2-1)(x-2) on [-1,2] find the point in the interval…

A: Given function is : fx=x2-1x-2 To verify the Rolle's Theorem and find the point in the interval…

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 linearization L(x) of f(x) at x = a. f («) — 4а? + 2а — 3, а — -5 -

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Q: Let f(x)= x2 − 6. Prove that the root of this function is equal to √6 {correct to 2 dp}, and lays…

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Q: If we apply Rolle's Theorem to the function f(x) = 2x² – 16x – 5 on the interval [2, 6], how many…

A: Given,          fx=2x2-16x-5 on the interval 2,6.We know that,         Rolle's theorem states that…

Q: Consider the following functions. f1(x) = 3 + x, f2(x) = x, f3(x) = x2 g(x) = c,f,(x) + czf2(x) +…

A: Let's find.

Q: Prove that the function f(x) = x3-3x2+3x-100 is increasing on R

A: Given function is : f(x) = x3-3x2+3x-100 We have to prove that f(x) is increasing on R

Q: Verify the Rolle's theorem for the function (x² – 1)(x – 2) on [-1,2] Find the point in the interval…

A: We can use application of derivative in order to solve the given problem.

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

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Q: Find c so that f is continuous at every point f(x) = 5x+12c, if x < -5 f(x) = (cx^2)+1, if x ≥ -5

A: Given- fx=5x+12c if x&lt;-5cx2+1   if x≥-5 To find- The value of c that  the above function is…

Q: Find the roots of the function f(x)=(2x-1)(x2+2x-3) with x belong to R

A: f(x)=(2x-1)(x2+2x-3)=0 We have find all the real numbers that make f(x)=0 because it is given that x…

Q: Find the value of k so that the function ( 5x +3 if x<3 f(x) = | kx² is continuous everywhere? if x…

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Q: At what interval of x will the function continuous, f(x) = { 3x²-x-2 x-1 0, x= 1 ", x#1

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Q: Let f, g:R R defined by if x 1 (x2 and g(x) = 3x + 2. %3D Find f-1 and g-1.

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Q: Verify the Rolle's Theorem for the function (x2 – 1)(x – 2) on [-1,2] find the point in the interval…

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Q: Show that the function f : N → N, given by f(x) = 2x, is one-one but not onto.

A: If f(x1) ≠ f(x2) then we get:

Q: 7 Find the most general function F such that F'(): - 5V?.

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Q: +1 Differentiate the function f (x) = In +1

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Q: Show that f is strictly monotonic on the given interval and therefore has an inverse function on…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: If 7х- 5,х <1 { h(x) = 3x2 – x , 1 < x< 3 Is h(x) continuous at (x=1)?

A: Continuity of function at a Point : Suppose a function f:A→B where A,B⊆ℝ .Then f is continuous at…

Q: Find

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Q: Use an (e – 6) argument to show that f : R →R be the function defined by 2 - 5x – 5 if I >-1 2+1+1 f…

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Q: Suppose that the function f: [0, 1]  in R is continuous and thatf (x)&gt;= 2     if 0 &lt;= x &lt;…

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Q: The graph of f(x)= x2 - 1 is concave down on interval | (-1,1) ^O (0,1) BO (-1,0) U (1, ∞ )co (- 00…

A: From the given problem:   fx=xx2-1   As we know that for concave downward:   f''x&lt;0   So,…

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

A: Solve the function

Q: Let f(x)={x2+2x+1, if x≤3 ax+b,if x>3 Find a and b such that the function f(x) is differentiable…

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Q: 3 Show that the function f(x) = Vx – 5 is one to one function. %3D

A: The objectives to show that the function f(x) is one to one function.

Q: 4 If f(x) = x 2 - function for all real values of x, then f(8) is equal to

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Q: Which of the functions below meet all requirements of Rolle's Theorem on the interval [– 4, 4]?…

A: follow next step

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: Prove that f(x)=x^3+x-1 has a root in the interval [0,2]

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Q: Find the function f(x) such that f' (x) = x²e# with f(0) = 0. O (x² - 2x - 2)e* + 2 O (x2 + x + 2)e*…

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Q: Find the value of k so that the function 5x +3 if x< 3 f(x) = - kx2 is continuous everywhere? if x23

A: we have to find the value of k where f(x) is continuous everywhere  Also find the domain in the next…

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: Consider the function f(x) = 2/x + 2 on the interval [4, 8]. Find th function on this interval.

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Q: Find the function g such that fog = In (2x° +7) if f(x) = In x g(x) = %3D

A: Find the function g such that  f(g(x))= ln(2x3+7) and f(x) = ln(x) .

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: For all x in the domain of the function –* , x+1 this func- tion is equivalent to:

A: Since you have asked multiple questions in single request,  So we will be answering only first…

Q: The domain of the function f(x)= cosh"'(x/ 3) is Select one: O[3,) O[0,3] O None O[-3,3 ] OR-{3}…

A: The domain of the function f(x): The set of values of x for which the function f(x) is defined.

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: C. Show that f(x) = (x26)² has no inverse on the interval (-∞,0).

A: Since you posted two questions here, i can answer only 1. Please reupload second question again.…

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: What values of a and b will make the function f continuous at x=2 and x=3? * x2 - 4 if x 3 2x – a…

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Q: Find the domain of the function using interval notation. f (x) = -2a (x – 3) (x – 5) | | To enter…

A: soution:-f(x)=-2x(x-3)(x-5)To find the domin of f(x)The domain of a function is the set of all…

Q: The function of f is increasing on I if ______ when x1 < x2.

A: We have to find when function is increasing

Q: 5. Find the value of k that makes the following function continuous. f(x) : ={2x - 1,if x2-1

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