Are the following statements true for all functions f and for all subsets A and B of the domain of f? () {f(x): E A}- {f(x): z E B} is a subset of {f(x): x € A - B} (ii) {f(x):x E A- B} is a subset of {f(x) : a E A} - {f(x):z € B} O Yes for (i). Yes for (ii). 47 OYes for (i). No for (ii). O No for (i). Yes for (ii). O No for (i). No for (ii).

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: For all functions f and g, f o g(x) = go f (x). O True O False

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Q: show that 1f ∘ g2 (x) = 1g ∘ f2 (x) = x.

A: Given: fx=1x, gx=1x. To find: f o gx=g o fx=x Solution: Finding f o gx. f o gx=fgx=f1x=11x=x

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: Find (a) the domain of  f and (b) f-1 and its domain.   f(x)  = In  (2 + In x)

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Q: f(x) =  2 x ,    g(x) =  x x + 2 Find the domain of  (f ∘ g)(x).  (Enter your answer using…

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Q: Let f(x) = x²-1 and g(x)= V15 – a Find the the natural domain o the function gof(x)

A: we have to find domain

Q: If f(x) = x + 8 and g(x) = x - 8, (a) f(g(x)) %3D (b) g(f(x)): %3D (c) Thus g(x) is called an…

A: Given,           fx=x+8           gx=x-8

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 both f(x) and g(x) be odd functions. If possible, determine whether each function must be even…

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Q: 25 – 3 Evaluate the domain of the function h(z) = 3 - z2 - i

A: The domain of a complex function f(z), is the values of z for which the function is defined .

Q: 2 Let f(x)=Vx and g(x)=- x-4

A: Given that  f(x)=√x and g(x)=2/(x-4) To find the f of g

Q: Let f be a function of x. f (x) = (x – 3)4 is an even function. - O True O False

A: Solution: The objective is to determine whether the given function is even or not

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: Evaluate (f o g)(¤) or f[g(x)] f(x) = 4x2- x +1 g(x) : - 4x 9 (fo g)(x) = flg(x) =

A:

Q: Given f={(-2,6).(-1,8), (0, 5), (1, 0), (2,-2)} and g(x)=x² +1, a) Graphf-g

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