Problem 5. a. For f: R→R given by f(x)=x-1, what is im(f)?>** b. For f: [0, 2)→ R given by f(x) = x-1, what is im(f)?

Q: suppose f (2) = 4, f ′(2) = 6, g(2) = −1, g′(2) = 3, and f ′(−1) = 5. Give h′(2) when h is defined…

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

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Q: 7. This problem requires calculus. Let P = {a,x" + an–1x"-1 + ...+ a1x + ao | n > 0, ao, . ., an E…

A: Given P is a set of polynomial function of degree n of real co-efficients and a function F:P→P such…

Q: Suppose that f is a function with f'(2) = −5. If u is very very close to 0, then f(2 + u) is…

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Q: 3. (b) Consider the function f(x, y) = a(x² + y²) + xy + 1 for some real number a. Find Vf. Find fxx…

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Q: 17. Given f (x) = -4, find f-(x). b. d. C. a. d.

A: The given function is

Q: 1. Let f(x)=x² - x, xeR then f(f(f(v2))) is: -34 + V2. b. 2/2 +34. c. 34+2/2. d. 34– 2/2. e. 2/2 -…

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Q: Given a, b E R. For which of the following f" (x) does y = f(x) have exactly one point of…

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Q: 6. Let f(x) be defined as follows: f(x) = {2f x is an integer (1 if x is not an integer Find each of…

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Q: 5. f() = {x? - 4 U x* -3 Evaluate f(4), f(0), f(-3) and f(-2/3) }" -2 if x = -3'

A: The objective is to evaluate f(4), f(0), f(-3) and f(-2/3).

Q: . Let f(x) = ka. Determine the constant a so that f(-1) = 10 and f(2) = 5 19 4

A: Given query is to find the constants of the function.

Q: Ax) %3D х* — Лх2 - 12x where A> = > — Лх? — ЛЕx where ^> v that fis one-to-one on S = [- rmine f(S).…

A: Given, fx=x3-λx2-λ2x,  λ&gt;0

Q: 11. Let f(x) = x³ - 2x² + x-1 so f(1) = -1 and f(2)= 1. Let g be the X inverse of f; that is, g(x) =…

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Q: 5. Let the derivative of the function f(r) be novin at dad FOLL 11 g(x)=x+ sin(x - 2) and ƒ(2+)-f(2)…

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Q: 4. If the function f(x) is defined by f(x) =-6 then which of the following is the value of f(10)?…

A: We solve using substitution

Q: If f be the function defined by f (x) = x³ + x. lf g (x) = f−¹ (x) and g (2) = 1, what is the value…

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Q: 1. Use the definition to find f'(e) if it exists *, if z< 3 S(x) = c= 3 -3r, if r 23

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Q: [2, 03 b) If f(t)={ , find L{S(1)}.

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Q: Let p = 37, and let f = x – 1. For each a in F,[r]/f, either find the inverse a why the inverse does…

A: note : As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly…

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

A: We need to find out first partial derivative

Q: 3. For f(x) = 15x²-3 16x²+9x+8 As x → ∞, y → || As x →∞, y →

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Q: 1. Let f(x) = 12 + 22 + 32 + .+x². Show f(x) is 0(x³).

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Q: 6. Let f be a function such that f(1) = 1, ƒ′(1) = 4, ƒ”(1) = −2 and ² ƒ""(t)(2 – t)²dt = 3. Find…

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Q: 6. Define f(x) = x³ – Ax2 – 12x where A> 0 is a constant. (a) Show that f is one-to-one on S =…

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Q: 5 2 7 . If f(x) = 3 + 4x · 2* + r", what are f"(0) and f"(0)? 3!

A: Given f(x)=3+4x-52!x2+73!x3

Q: 4. If f(x, y)=In(2x + 3 e), then- af axy for this function is

A: Find the partial derivative for the function f(x,y)=ln2x+3ey

Q: 2. Let f(x) = -x– 1. a) Find f-1(x).

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Q: 6. Given that f(x) = 3x? + 1, find +h)=[(x)

A: Given f(x)=3x2 + 1

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: 6. The starting point of f(x) = -23(x – 4) – 8 is А. (2,-8) В. (4,8) С. (-4,-8) D. (4,-8)

A: To find the starting point of a function, first, we find the domain of the function. The starting…