Suppose that F(x) is a function such that F"(x) = f(x). Which of the following statements is true? [ f(x) = F(b) – F(a) ·b [ f(x) = F(a) – F(b) ·b [* F(x) = f(b) – f(a) - [*F(x) = f(a) – f(b)

Q: Show that if f1(x) and f2(x) are functions from the set of positive integers to the set of real…

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Q: If f(n) and g(n) are multiplicative functions, and g(n) does not equal 0 for all positive integers…

A: Definition 1 : A function f: ℕ→ℂ is said to be arithmetic function .   Definition 2 : An arithmetic…

Q: If f1(x) and f2(x) are functions from the set of positive integers to the set of positive real…

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Q: f is a function of all real numbers defined by f(x)=x2, what is f-1({x |0<x<1})?

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Q: Let f(x) = m1x + a and g(x) = m2x + b, where m1, m2, a, and b are constants. Determine the necessary…

A: f∘g=g∘ffgx=gfxfm2x+b=gm1x+am1m2x+b+a=m2m1x+a+bm1m2x+m1b+a=m1m2x+m2a+bm1b-b=m2a-abm1-1=am2-1

Q: Let f be a function with the following known values f( – 1) = 1, f(0) = – 4, and f(3) = 5. %3D Let g…

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Q: - If x² - x f(x) g(x) = x and X - 1 is it true that f = g?

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Q: Let g be the function g(x)=x²-x. Find g(-a). O None of these. O-a² + a O a² +1 O-a²-a O a² + a O…

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Q: a. Determine whether f(x) = 5/(x+1) is a one-to-one function from R to R, if not, give a counter…

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Q: Let f(x) and g(x) be functions. Prove, using contradiction method, that if f(g(x)) is one-to-one,…

A: We have , f(x)  and g(x) are two functions.  We know the definition of one-to-one function, suppose…

Q: Express the function F in the form f ∘ g ∘ h. (Enter your answers as a comma-separated list. Use…

A: first we analysis to given question that how to find f, G, h then we compute F(x) function.

Q: Determine F(x) if, for all real x and y, F(x)F(y) – F(xy) = x + y.   Hint:  What could F(1) be?

A: Consider the provided question, We have to find F(x).

Q: Let f(x) f-¹(-2) = x + 3 x + 6

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Q: XI. Refer to the functions f, g, and h defined here. f(x) = 1/x, g(x) = 2 vx, and h(x) = x2 -1…

A: Using rules of functions.

Q: 3. Show algebraically that the function f (x) x* – - 2x + 5 has even, odd or neither symmetry.

A: To find out that the function has even, odd or neither of these symmetry.

Q: Suppose f is a real function satisfying f(x + f(x)) = 4ƒ(x) and ƒ(1) = 4. What is ƒ(21)? f(21)=

A: Suppose f is a real function satisfying f(x+ f(x))= 4f(x) and f(1) = 4, what is f(21)?

Q: 1. Let f(r) and g(a) 4x + 1. 4 Then (f o g)(6) (ƒ o g)(x)

A: We have to find function

Q: Let f1(x) and f2(x) be functions from the set of real numbers to the set of positive real numbers.…

A: Big-O Notation:Definition: Let f and g be functions from the set of integers or the set of real…

Q: Prove that, if f(x) and g(x) are any functions of x, (i (i (ii. f(x) 8 (x) A f(x) - f(x) A g(x) (iv)…

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Q: Let f(x)=x2, g(x)=2x+5, and h(x)=x2-1 a. h[f(-2)] b. f[g(x-1)]

A: Given that , fx=x2 gx=2x+5 hx=x2-1

Q: Which of the following is the domain of the function g(x) 2-x 0(-00,2 O (-00, 0) O [0, ∞0) O (-0, 2)

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Q: Let f(x) = 1 and g(x) +4. Then (fo g)(æ) (go f)(x) =

A: (f o g)(x) = x/6 (g o f)(x) =(4x -10)/(x-4)