a) f(x) < 0  b) f(x) ≤ 0 c) f(x) > 0 d) f(x) ≥ 0

Q: 8) For f(x) = x +1 and g (x) = 5x + 4, determine the following. a) 4 points h (x) = (f •g)(x). b) 4…

A:

Q: 4. Let f(x)=1+x³-x. Find an x-value that makes f(x) 0.

A:

Q: 8. Find f-1 (x) for f (x) = 2-4

A:

Q: 2+x 5. Given f(x) =<tX Find X-4 %3D a) fe) b) f(a+1) c) f(x) + f(h)

A:

Q: 2.if f (x) = x2 + 3, with domain R then f(x) has f(x) %3D O T F

A: Here the given function is f(x)= x2+3 with domain R We need to find it has inverse or not.

Q: For the function f(x)=√x+3 ifx<2 2x-3 ifx22 evaluate the following: ,

A: Function f(x) is two different value of different value of x

Q: Find the values and expressions in parts a through h for the function f(x) = /x< +5x. (a) f(0) (b)…

A: Since you have asked multiple subpart,as per our guidelines we are supposed to answer only first 3…

Q: 6. Use algebra to determine whether the given functions are is even, odd or neither a) f(x) = -x³ +…

A: For a given function f(x)  If it satisfies the condition  f(-x) = f(x), then the function is Even.…

Q: - h)? + k: a). f(x) = 2x² –12x+11; b) y = -r+x+:

A:

Q: 10) Calculate; Let f(x) = 3x + 1, g(x) = 4x-7 a) f(3) + g(4) b) f(x)-g(x) c) f(2)* g(-3)

A:

Q: True or False.   If f(x) = a * x ^ 3 + b * x ^ 2 + cx + d where a 0, then f has at least one…

A: Given that: f(x)=ax3+bx2+cx+d, a≠0

Q: IfY C X, show that inf (X) < inf (Y)

A:

Q: 11) For the function f(x)x+3 a) Find f(1) and f(m +6) b) Find the domain

A: We have been given a function and we are supposed evaluate its value for the given value/expression…

Q: (-x if x < -2 4. Let f(x)=x² if-2<x<2 Compute the following function values: (0 if x ≥ 2 a) f(-3) b)…

A:

Q: Consider these functions. 1) Evaluate (f + g)(2). f(x) = 3x² – 5 g(x) = Vx - 2 A) -1 B) 0 C) 3 D) 7…

A: we have the given functions  f(x)=3x2-5 g(x)=x-2 1) (f+g)(2)=f(2)+g(2)…

Q: What is true about the function f(x)= = a) f(x) → from above b) f(x) →2 from above c) f(x) → from…

A:

Q: 5. Let f(x) = 2x³-x² +7, find: a) ƒ(2) b) f(-5) c) f(a)

A: “Since you have posted multiple questions with multiple sub parts,we will provide the solution only…

Q: 3. Given f(x) = x²?+ 2x and g(x) = 2x - 10, determine: a) (f + g) (x) g(x) b) c) (f og)(x) f(x)

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Q: 5. If f(x) = 2 x + 3 a) f-¹(g(x)) and g(x) = 21, find b) the domain and range of f-¹(g(x))

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Q: Which of these functions has a y-intercept of (0,9) ○ A) ƒ(x) = 9x² + 4x + 2 B) f(x) = 9(x-3) (x +…

A:

Q: 4. For f(x) = x² – 3x, evaluate a) f(2) [2,3,3] c) the value of x when f(x) = 4 b) f(m + 1)

A: Given,              f(x)=x2-3x

Q: ,x2

A:

Q: Find where f(x) = 1-ax x(x-a)(x+b) is discontinuous.

A:

Q: Why is fnot a function from R to R if a) f(x) = 1 f(x) is not a function because when x = is…

A: In this question, we will show that the given f is not a function.

Q: Express the function h(x) f(x) ‡ x and g(x) ‡ x. a) g(x) = = X 1 x - 1 in the form h(x) = = b) f(x)…

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Q: 2х f(x) = ,x 1

A:

Q: 5. Determine f,(x); f(x) = x*², x > 0

A: We need to find out first partial derivative

Q: 6. Let f(x) = x − 1 and g(x) = (x + 2)², find the following: a) Domain of f(x) b) Range of f(x) c)…

A: "Since you have posted a question with multiple subparts, we will solve the first three subparts for…

Q: Let f(x) = Vx and g(x) = x³ +1. Find 29 a) f(g(2)) b) g(f(4)) c) f(F(16)) d) g(g(0)) e) f(2+ h) f)…

A:

Q: 8. Simplify f(x + h) - f(x), where: a) f(x) = 2x + 3 b) f(x) = 1 c) f(x) = x² %3D 1 2.

A: a) f(x)=2x+3b) f(x)=x2c) f(x)=11

Q: 4 2. Use f(x)=x². -3 x - 7 to answer: (a) f(0) 2 < x < 6 -2 < x < 2 otherwise (b) f(2) (c) ƒ(5)

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.