Given f(x) dx = 6 and g(x) dx = -4, evaluate the following. %3D (a) [f(x) + g(x)] dx (b) [g(x) – f(x)] dx (c) 2g(x) dx (d) 3f(х) dx

Q: Var(5 + 2vx) = 4(E(x) – (E(Jx))² true False O

A: From the provided information, Var (5 + 2√x) = 4(E (x) – (E(√x)))2

Q: Given f(x) = x² + 3x + 9, find the following. HINT %3D (a) f(0) (b) f(1) (c) f(-1) (d) f(-3) (e)…

A:

Q: If ​f(x)= 2x2 −5x+3​, find f′(3).

A: To find f'(3)

Q: f(x) = xe-2x

A: Step 1: Step 2: Step 3: Step 4:

Q: f(x)=-6x+3 find f(1/2)

A: Given: fx=-6x+3 To find: f12

Q: f(x)=4x-x2. Simplify f(a+h)-f(a)/h

A:

Q: If f(x) dx = 5x³ – 7x6 + C, find f(x). f(x) =

A:

Q: Let f(r) = 4x + 2 and g(z) = 5a² + 5x. After simplifying, (fo g)(x) =

A:

Q: f(x) = 9 – x2 (a) f(x + h) – f(x) f(x + h) – f(x) (b) h

A: Put x=x+h in f(x)

Q: If f(x) = 2x + 3x – 1, evaluate the following. %3D (a) f(a) (b) f(-a) (c) f(a + h) f(a + h) – f(a)…

A: Given, fx=2x2+3x-1 a) fa is found as follows: Substitute a for x in the given function.…

Q: If f(x) dx = 3x8 - 5x + C, find f(x). f(x) = %3D

A: The given integral is ∫fxdx=3x8-5x4+C

Q: For f(x) = -3x² + 5x 2, find %3D f(x + h) – f(x) h+ 0 h

A: fx=-3x2+5x-2

Q: Find f(9(x)) when f(x) = 2x +1 and g(r) = 2? +

A: On solving this we will get

Q: 1 and g(x) x – 7 Let f(x) +7. Find and simplify the following: (a) (ƒ o g)(x) (b) the domain of (ƒ o…

A: As per our guidelines we are supposed to answer one question , kindly repost the remaining question…

Q: If f(x) = x2 + 3x - 1, find:

A: Given:fx=x2+3x-1fa+h-fah

Q: Use the functions f(x) = 2x + 5 and g(x) = 3x² to calculate each operation and simplify, if…

A:

Q: d -(f(x² + 3x)) dx

A: Derivative

Q: s(2) dr=3 and s (4)d. f (x)dx: =-2. what is (x)dx? Make sure to justify your answer -2 or the…

A: We can find the answer as below using property of integration.

Q: Find the inverse of f(x) = 2x + 7.

A:

Q: 4a+ax/x)=f a=

A:

Q: If  f(x) = 4x2 − x3,  find  f ′(x),   f ″(x),   f ‴(x),  and  f (4)(x)

A: Topic- derivative of a function We are given, f(x) = 4x2 − x3 and we know thatddxxn=nxn-1

Q: If f(x) = x - 3 and g(x) = x² + 4, simplify (f g)(x).

A: We know, (f∘g)(x)=f{g(x)} Gvbhj