2.12.2: Composition of functions on integers. Consider three functions f, g, and h, whose domain and target are Z. Let f(x)=x2           g(x)=2x           h(x)=⌈x5⌉   (b) Evaluate (f ο h)(52) (c) Evaluate (g ο h ο f)(4)

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: The table contains some input-output pairs for the functions f and g. x f(x) g(x) 3 10 6 4 7 10 6 3…

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Q: 2. Which shows that f(x) = 5x² -2 and f-¹(x)=√√2 are inverse functions? O522 -2= *52…

A: If f(x) and f -1(x) are inverse functions then  (f∘f -1)(x)=(f -1∘f)(x)

Q: 3. If the function f : R R is defined by the rule f (x) = 4x + 1 for all real numbers x is…

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Q: Consider the recursively defined function: f(0) = 2 , f(n) = 2f(n-1) +5 where n   is an integer…

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Q: Refer to the following functions: p(x) = x² + 2x – 15 x+1 q(x) = x - 3 r(x) = v7-x Which of the…

A: Given functions are px=x2+2x−15, qx=x+1x−3 and rx=7−x. We have to check whether the given statements…

Q: 1. Refer to the given functions f, g, and h to evaluate the functions for the given values of x.…

A: a. As (f-g)(-1) = f(-1) - g(-1) So (f-g)(-1) = [(-1)2 - 3(-1) + 1] - 8 - (-1)                = 1 + 3…

Q: Let f:R → R be the function with rule f(x) = 5x + 2, and let g: R → R be the function with rule y –…

A: To find  f0g(-1)  And  f0g(6)

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: Use the graphs of f and g (see attached) to evaluate the composite function : (g ∘ f)(0)

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Q: Let n be a nonzero integer. Find a domain on which the function                       f(x) = (1 -…

A: Let f(x)=y. Then y=(1-xn)1/n. In order to write the inverse function expression write x in terms of…

Q: Consider f (x) = 2/x and g (x) = x + 3. Determine whether the domain of fg is the same as the domain…

A: Find the domain of g and domain of fg seperately and compare them that they sare same or not.

Q: Suppose that the function g is defined, for all real numbers, as follows. 1 -x+2 if x #1 g(x): -3…

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Q: Suppose f and g are two functions with nonnegative values. If f(n) is (n) and g(n) is (n³/2), then…

A: We have given that , f and g are two functions with non - negative values. If fn is θn. Also , gn is…

Q: 2² – 7x + 12 Explain why f(x) = x – 4 is not the identical function of g(x) :

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Q: 4. Consider the function if x > 0 {2 if a < 0 g : R – R, g (x) = -2x2 Is this function bijective?…

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

A: Remark: we know that (f•g)(x) = f(g(x))

Q: (c) Let U be the set of natural numbers, A be the set positive odd integers and B be the positive…

A: Let's find.