Let ƒ(x) = ax + b and g(x) = cx + d. What condition must be satisfied by the constants a, b, c, d in order that (ƒ ∘ g)(x) = (g ∘ ƒ)(x) for every value of x

Q: Let f(x) =(x-1)(x-2)(x-3),Prove that there is more than one "c" in (1,3) such that f'(x) =0

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Q: A function f is choice of x1 and x2 in I, with xi<x2, then f(x) <f(x2). on an interval I if, for any

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Q: Let f(x) = 11x – 3, and g(x) = x3 – 8.  Find (gof)(x).

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Q: Let f(0) = 3 and 2 ≤ f′(x) ≤ 4 for all x in the interval [−5, 5]. Determine the greatest and least…

A: Using mean value theorem we get: For some x between 0 and 2

Q: If f(x) = x + /2 – x and g(u) = u + v2 – u , is it true that f = g?

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Q: If f(x) = 4x2 + 1 satisfies Rolle's Theorem on [a, 2], then a = 2 -1 -2 none

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Q: Show that for all x>0, e* >1+x+÷ 2.

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Q: #: Let X₁, X₂, ..., X₁ ~ f(x) = {0x0-1 0<x< 1 find Suff. Comp. St. " e.w.

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

Q: Prove that the function f:Q Q given byf(x) = 2x – 3 for all x E Q is bijection

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Q: Verify if the function f(x)= x² – x – 30 satisfies criteria stated in Rolle's theorem on [-5, 6 ]…

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Q: If f'(x) and g'(xr) exist and f'(x)>g'(x) for all real x, then the graph of y = f(x) and the graph…

A: Given: Let and exist and for all real x,

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A: we have to fill the following blanks ;  The domain of f/g consists of numbers x for which g(x)…

Q: . Show that exp(m1 x), exp(m2 x), and exp(m3 x) are linearly independent functions, where m1, m2,…

A: Part (A): There are three functions, now we have to find the function is linearly independent or…

Q: Let f(x) = 2x +3, g(x)= x- 4, and h(x) = 4x- 1. Compute (fo ho g)(2).

A: Here we have to find the composite function.

Q: A function f is ___________ on an interval I if, for any choice of x1 and x2 in I, with x1 &lt; x2,…

A: To fill: The blank of the statement. Given: The statement is "A function f is _______ on an open…

Q: Let k(x) f(x)g(x) h(x) If f (x) = 3x, g(x) = x - 2, and h(x) = -x² + x + 1, what is k' (x)? %3D…

A: We know that, from quotient rule of differentiation We have,  fx=3x, gx=x-2 and hx=-x2+x+1 Now,…

Q: If f'(x) and g'(x) exist and f'(æ) > g'(x) for all real æ, then the graph of y = f(x) and the graph…

A: f'(x) and g'(x) show the slope of function  so here given that slope  f(x) &gt; g(x) so they do not…

Q: Prove that F (3.x)(A → B) → (Vx)A → (3x)B. 3.

A: To prove: ⊢∃xA→B→∀xA→∃xB

Q: Let k(x)=f(x)g(x)h(x). If f(x)=−3x+4,g(x)=−x+4, and h(x)=−3x2−4x+3, what is k′(x)?

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Q: Find the points c (if any) such that f '(c) does not exist. f (x) = x2/3

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Q: Let f(x) = 2x +3, g(x) = x – 4, and h(x)= 4x – 1. Compute (h o go f)(3).

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Q: that satisfy f(x) = x³ + x – 1, [0,2]

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

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A: Use rolle's theorem As per guidelines only first question solve raise another queu

Q: Find f such that t'(x) = x - 2 and f(0) = 6. f(x) = O

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Q: Show that if f and g are linear, then so is f + g. Is the same true of f g?

A: Let f,g:V→V are linear maps To show that f+g and fog are also linear

Q: If f(x)=/2x and g(x)=1-x², then (gof)'(x)= %3D

A: =&gt;(g.f)(x)=g(f(x))

Q: Let f(x) = 4x + 9, x, =2, x2 = 3, x3 = 4, X4 = 5, and Ax = 1. %3D (a) Find Ax. i= 1

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Q: Let h(x) = f(x)*g(x), and k(x) = f(x)/g(x). g(x) has points (-2,-1), (-1,-2), (1,0), and (3,2). f(x)…

A: see below the answer

Q: c. f(x) = (-1 if x 0 %3D

A: We need to find possible points of discontinuity.

Q: If f'(x) and g'(x) exist and f'(x) > g (x) for all real x, then the graph of y = f(x) and the graph…

A: In this question we have to find if the graph will intersect or not.

Q: If g(y) is differentiable for 2 < y < 3 and g(2) = g(3) = –-1, then there is some 2<a< 3 such that…

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Q: If f(x) = x + V2 – x and g(u) = u + v2 – u, is it true that f = g?

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Q: Find the zeros of the function: p (x) = (2x – 1) (x² – 4x + 5). - , 1, 5 1 O - 1, 1 2 - i, 2+ i 2 1…

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

Q: Let f(x) = x² + Vx & g(x) = x2 determine (fog)(x) & (gof)(x) and its domain

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Q: f(x) = 2x, g(x) = 3x², h(x) = 5x – 8x²

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Q: If g' (x) = Ofor all values of x in the interval (a, b), then g is a constant function. True False

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Q: For a function g(x), if there exists x E [a,b] such that g'(x) > 1, then we conclude that g(x) has…

A: Solution: Given, gx is a function and there exists x∈a,b such that g'x&gt;1. Then, gx has not a…

Q: Find f(x) and g(x) such that h(x)= (fo g)(x) and g(x) = 1-8x. h(x) = (1- 8x)3 - 3(1 – 8x)2 + 7(1 -…

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Q: f(x) = x³ – 3x²

A: Given: f(x) =x3 -3x2 -9x +27

Q: 12. Let f(x) = x + 2 and g(x) = x² - 1. Find (gᵒf)(4)

A: Given two functions 1.f(x)=x+2 g(x)=x^2-1 lets find g(f(x)) at 4

Q: Suppose that Y = Z - X is independent of Z and of X. Show that Y is a constant.

A: Given that Y=Z-X. To show: Y is a constant function.

Q: Let f(x) = x2 and let P = {-2, -3/2, -1, -1/2, 0, 1/2, 1 }. Compute Lf (P) and Uf (P). Lf (P) =  Uf…

A: Given, fx=x2P=-2,-32,-1,-12,0,12,1 Formulas used: LfP=∑i=1nmixi+1-xiUfP=∑i=1nMixi+1-xiWheremi=inf…

Q: 4) Show that and are eventually fixed points for the function : 8 4x Osx< 2- 4x sx< f(x) = - 1 4x –…

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Q: Let f(x) = x4 − 2x2. Find all values of c in the interval (−2, 2) such that f′(c) = 0.

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Q: If g (x) =3x²– 4x+5 ; G(x)=x³– 2x²+ 5x , then G is the anitiderivative of f . A True B) False

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Q: Find  a and b  such that the function f(x)={x^2+4x+8 if x_&lt;1         {ax+b if x&gt;1

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Q: Suppose z is a function of r and y, and x² + y² + z² = xe² + ye² + ze³. Solve əz əz for and əx ду

A: Topic = Derivative

Q: Express ax? + bx + c as a linear combination of the functions f(x) = 5, g(x) = 4x, and h(x) = -x²,…

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Q: let f(x)={x^2+2, x >-1 AND -x^2-x, x less than for equal to -1} compute f(0), f(-1)and f(-2) a. 0,…

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Q: Verify if the function f(x)= x² – x – 30 satisfies criteria stated in Rolle's theorem on [-5, 6 ]…

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