Suppose that f(x) =x², x20, and g(x) = x, x20. Typically, fog gof, but this is an example in which the order of composition does not matter. Show that fog=gof. Which of the following is equivalent to (fo g)(x)?

Q: For f(x)=2X2 and g(x)=x+1 , find the composition (f  o g )(x) = f(g(x)).

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Q: Given the functions fAx) = x - x and g(x) = x- 1, determine an equation for the combined Ax) y =…

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Q: Graph the function f(x) = u₂(x) ln x + u5(x) (ln(10 − x) – In x) -

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Q: Find (f=1)'(a). f(x) = 5 + x2 + tan(Tx/2), -1 < x < 1, a = 5 (F-1)'(a) =

A: NOTE: Refresh your page if you can't see any equations. . take x=0 and check  so the point…

Q: Given g(x) = In(7x5 + æ), the derivative g'(x) is 5x4 35x4 +1 7x5 + I O 7z5 +x 7x +I 35x4 +1 O 35x*…

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Q: If f(x, y) = In (2x-3y), then find of ||

A: We can solve this problem using partial derivatives.

Q: Let h(x) = f(z) where f(x) = ln(3x² + 2x +2) and g(x) = -2x. What is h' (x)?

A: hx=fxgx=ln3x2+2x+2-2xf(x)=ln3x2+2x+2 Differentiate f with respect to x…

Q: Given that f(x) =x+4 and g(x)=x -x, find (f+g)(1), if it exists. -X,

A: Given two functions f(x) and g(x). Then (f+g)(x)=f(x)+g(x)

Q: Ex/ show that f(x) = x+7x + 4 x + 1 has an inverse. %3D

A: In this question we have to find whether the function has an inverse.

Q: 2. If f(x) = x - 3 and g(x) = x2 + x, what is the composition g(f(x))? a) x2 + x + 9 b) x2 - 5x…

A: A function is a relation which maps each value in its domain to exactly one value in its range. The…

Q: 1. Find the composition function a) y =f(x) = b) y = f(x) = 2x + 5x2

A: a)  given   f(x) = 1x Thus composition function of f(x) = g(x) = f{f(x)} = 11x = x

Q: Find f(x) iff, (p) Hence deduce F .

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Q: 5. If f(x) = 2x² - 3 and g(x) = 2 sinx, determine (fog)(x) and (fog) (), 0≤x≤ 2n.

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Q: Express h(x) as a composition of two functions: h(x) = 3√(x2 + 1)

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Q: ) Find the values of the constant a so that the function f (x) will be continuous for all x. fax +…

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Q: 2. If f(x) = 1 + x², find fof 3.lf f(x) = -x, g(x) = 2x + 1 and h(x) = x², find fogoh,

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Q: find a general formula for f (n)(x). f (x) = x2e x

A: The first derivative of a function when equated to 0 gives us the critical points of the function…

Q: Given that f(x) = 3x – 1, g(x) = 2x and h(x) = x + 1, determine: a. hgf(x)  b. hgf(-2

A: Given : f(x) = 3x-1             g(x) = 2x             h(x) = x+1  To Find : hgf(x)…

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: e. As x+, y =-3 x+2x-3x* → f. As x-2, y=4+5x →.

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Q: If f(x) = In( 3 + e4x ), find f '(0). f '(0) =

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Q: Let g(x) x2+4. Find a function f that produces the given composition (fo g(x)= x+8x2+27

A: (fog)(x) means f(g(x)). Plug g(x)=x^2+4.

Q: 7. Let f(x)=64x² ln (2x) −16x¹. Findƒ(e)-f(€) 2

A: NOTE: Refresh your page if you can't see any equations. . take x=e

Q: Find the convolution of (a) Ila * IIa. (b) f(x) * f(x), where f(x) = e-l=l, -0 < x < o. %3D

A: Convolution : The convolution of two functions f(x) and g(x) is given by f(x)*g(x)=∫-∞∞f(y)g(x-y)dy…

Q: If f(x) = 4-x & g(x) = Vx them find (fog)co (gof)

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Q: Which of the following is an antiderivative of f(x) = 12x³ - 9x2 + 8x – 3?

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Q: Differentiate the following f (x)% 3sin-(e9) %3|

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Q: Let h(x)=f(x)g(x), where f(x)=ln(4x2−3x) and g(x)=3x−1. What is h′(x)?

A: GIVEN,     f(x) =ln (4x2-3x)                  g(x)  = 3x-1                  h(x) = f(x) g(x)

Q: Suppose you have just finished approximating f (x) = x3 for 0 ≤ x ≤ α and ended up with φˆ(α, x) =…

A: Given suppose you have just finished approximation f(x) =x3 for 0≤x≤α and ended up with φ^ α, x=…

Q: Let h(x)=f(x)/g(x), where f(x)=ln(3x2 +2x+2) and g(x)=−2x. What is h′(x)?

A: Here we use quotient rule, which is pq'=p'q-pq'q2

Q: find three functions, h(x), g(x) and f(xr) so that K(x) is the composition of h, g, and f, in other…

A: We will use the concept of composition of functions.

Q: let f(x) = (6x+3) and g(x)=(-2x+5) *use chain rule to calculate h'(x) where h(x)=f(g(x)

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Q: Let f(x) = 4*(1 - x/2); 1 ≤ x ≤ 2.   Find E(x). Find exact value (use fractions).

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Q: find the most general antiderivative of f(x)=6x^5-8x^4-9x^2

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Q: 2. If f(x) = x - 2 and g(x) = x2 + 2x, what is the composition g(f(x))? A) x2 - 2x B) x3 - 4x…

A: Given  f(x)=x-2g(x)=x2+2x To find g[f(x)]

Q: If f(x) = cosh-'(5x), then f'(x) %3D

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Q: For the real-valued functions f (x)3D2x-1 and g (x) =Vx-4, find the composition f og and s

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Q: Find each f(c) using synthetic substitution. 12. Ax) =5x + 10x* + 3x + 8x² – 6x – 3; c = 3 (SHOW…

A: Concept - we have given a function F(x) , and asking about C=3 ,so substitute c in given…

Q: Suppose that f(x) is O(g(x)). Does it follow that 2f(x) is O(2g(x))?

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Q: Discuss the monotonicity of g (x), where g(x) = 2f + f(6-x) for all x e R. 2

A: Test for monotonicity:           let us consider a function is continuous on [a ,b] and it is…

Q: If f(x) = 5x - 2, g (x) = – 2r + 3 and h (x)= x, then (fogoh)(-2)=.... %3D

A: The functions are f(x)=5x-2g(x)=-2x+3h(x)=x3 If f(x) and g(x) are two functions then the composition…

Q: 4. For f(x) = 3x² + 5 and g(x)=7x-2, %3D %3D

A: answer is in next step

Q: 02. Find the end behavior for y = x–9x+20. A. x + +0, f(x) → +∞ ; x → -o, f(x) → +∞ B. x → +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 the requested composition functions.  given f(x)=4x^2+3x+6 and g(x)=3x-4, find (gof)(x)

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Q: 1. If f(x) = 3x + 9 and g(x)=x²-4, find: a) (fog)(x) c) (gof)(x)

A: A detailed solution is given below

Q: 6) Find the value of c such that {0, c} is 2-cycle such that c be a constant and let the function be…

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.