If f(x)= x2 – 2x-3 & g(X) = |X| thenfind: a) (fog)x) & b) (gof)x)

Q: (b) ruz – 2yuy + u = eª , for x> 0

A: 1.(b) Given partial differential equation xux-2yuy+u=ex, for x>0 This can be written as…

Q: 1 Find Vf if f = 2 /x²+y² +z?

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Q: (B) let y = 3sin5x - 2cos5x show that ax y + 25y = 0

A: Given :y=3sin5x-2cos5x

Q: Show that r: y = 3. 2n

A: Using two sectant theorem,  ∠n=12x-y  Multiply both sides by 2. ⇒2n=x-y .....(1) Using intersecting…

Q: The productivity of a country is given by ​f(x,y)=14.41x0.427y0.573​, where x is the amount of…

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Q: df If f(x, y) = x² + 2x – 1, then 0. - ду True False

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Q: 1 If y = V1-x then y' = 2/1-x

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Q: art of z- 2z, if z = a+ib ?

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Q: Show that Y1 = X1/X2 and Y2 = X1 + X2 are independent and that Y2 isχ2(r1 + r2).

A: Given Y1=X1X2Y2=X1+X2

Q: 4.3 Verify that for f(x, y) = 4x°y$ - 9x*y³. дх ду ду дх df

A: Explanation of the answer is as follows

Q: 10. If f (x) = 2x(1+In(2x)), and f'(c) = 6, find c.

A: Given function is fx=2x1+ln2x. Product rule of differentiation states that: ddxuv=vddxu+uddxv…

Q: Let A = %3D {x €N|2 < x < 7|} . What is n(A)?

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Q: If f(x, y) = 2x+6 (2a-6y) of then is given by:

A: In the above question we will take y as constant since we have to partially differentiate it with…

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

A: We can solve this problem using partial derivatives.

Q: (b) Let f(x)=√x and g(x) = 2x+5, find: (1)fog(x) (2)gof(x)

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Q: 4 Suppose that f(x, y) = x4 + y xy

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Q: (b): Let f(x) V3x +9 and g(x) = 2x + 6 find fog(x) and gof(x).

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Q: If f(2) = 15 and f (x) > 2 for 2 s x s 4, how small can f(4) possibly be?

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Q: Maximize B=6xy^2​, where x and y are positive numbers such that x+y^2=4.

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Q: If f(x, y) = 4x² – 7xy + 3x, then is given by: af - O 8x 8x – 7x + 7y + 3 - O 8x 8x – 7x – 7y + 3 -…

A: The solution of the problem is given in the next step.

Q: Let h(x) z² –3z+2 -z² –4x+4' what is h' (-5)?

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Q: If f(z) = 5.7x +6.9, then, f(x+h) is:

A: Given : fx =  5.7x+6.9

Q: Q 4. (a). Show that fog = 4x² - 1, if ƒ(x) = 4x – 5 and g(x) = x² + 1. (b). Show that gof = x + 4\x…

A: Given, f(x)=x+2,g(x)=x2+6 To show: gof=x+4x+10 Solution: f(x)=x+2,g(x)=x2+6 We know,…

Q: For what values of x is Ax) concave down if f "(x) = 3x' – 14x² + &r?

A: Given that, f''x=3x3-14x2+8x For what value of x is fx concave down.

Q: Q 4. (a). Show that fog = 4x² – 1, if ƒ(x) = 4x – 5 and g(x) = x² +1.

A: a. Given: The functions fx=4x-5 and gx=x2+1, To find: f∘g=4x2-1, Formula used: (f∘g)(x)=f(gx).

Q: Let / (r) – = 2x 3z+2 and g (r) 6x 5x+2. What is the rule for (g-f) (x)? o (g-) ()- 4 2x o (g-) (2)…

A: Given functions are                                   f(x)=2x4-3x2+2g(x)=6x2-5x+2 we have to find…

Q: Let F = Z, [x] (x³ + 3x + 2) and α=x+ (x+3x+. (x³+3x+2) €F. Find a³.

A:

Q: Suppose that W (y1, Y2) (t) = 4, and y3 Yı – 3y2. What is W (y1, Y3) (t)?

A: Correct option -12 We have to find out the value for Wy1,y3t.

Q: Suppose 3x2 – 3x + 8 - f(x) : x (x2 + 4) Then A f(x) Bx + C | x² + 4 where A = and B %3D , and C =

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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

A: Let's find.

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

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

Q: on f(x) = +9x is %3D 2)

A: There are multiple questions, as per company policy kindly ask other questions separately.    Given

Q: 3. y = x³ – 3(x² + w²) 4. y = x7 + V7x - 1 TT + 1

A: Differentiation wrt x

Q: II. Verify that ду дх дх ду 3 2 2. f(x, у) %3Dх'у? — ху 'y² – xy ³

A: Given function: Now,

Q: . What is F(/3) if C = 0?

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Q: is given by: If f(x, y) then 8(8x-4y) '

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Q: *宗+> B. If z = show that x 3z %3D x+y

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Q: |(-m,-풀) -꿀 | (-풀,0) (0. 풀) (5. ") f(x) f '(x) f "(x) Concavity

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Q: Q2) Show that y = 35 x* – 30 x2 +3 satisfies ( 1- x² )y" – 2xy' + 20y = 0 %3D

A: y =35x4 - 30x2 +3 satisfy (1-x2)y" - 2xy' +20y =0 for this wew find  y" and y' y' = 140x3 - 60x y" =…

Q: Suppose that X is a (A = e-100, p = 3e-100)-BCP. %3D What is P(X(1)X (2)X(3) = 4)?

A: Correct answer is 4.

Q: If x &lt; 0 and y &gt; 0, determine the sign of the realnumber. x2y

A: Given, The real number is x2y.

Q: The discriminant of ax2 + bx + c = 0 is defined by_________.

A: The given equation is ax2+bx+c=0.

Q: 23) The domain of f(x) = Vx + 3 is

A: Consider the function

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: Eliminate the arbitrary constants of: x^2=Axy+By

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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: Suppose that f(x, y) = 4x + y on the domain D = {(x, y) | 1 < x < 2, a < y < 4}. D

A: Solution is in step 2

Q: ,2,,2 Suppose that f(x, y) = 10x²y² + 6x? + 2y? then find the discriminant of f.

A: We have to find the discriminant from the given function

Q: Sınx SecX - Sen xcsc x ta n x-

A: Let the trigonometric identity given in the question be, sinxsecx-sinxcosecx=tanx-1. Some of the…