Consider functions f: {1,2,3, 4} → {a, b, c}. i. How many such functions are there? ii. How many such functions have a single output? iii. How many such functions are surjective (i.e. have all three outputs)? iv. How many such functions have exactly two outputs? (Hint: you can compute this directly, but it may be easier to combine your answers from the previous parts.)

Q: Find f ∘ g, g ∘ f, and g ∘ g. f(x) = x2,    g(x) = x − 1 a). f ∘ g ?     b). g ∘ f?     c). g ∘ g?

A: Given f(x) = x2,    g(x) = x − 1

Q: Consider a function machine that accepts inputs as ordered pairs. Suppose the components of the…

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Q: d) Is the composition of two one-one functions a one-to-one function? e) Is it true that P(A) ≤ A?

A: For part (d), the answer is YES.

Q: Let f: R+N+ with f(x) = [x²]; that is, f(x) returns the square of x rounded up. Characterize f in…

A: I have explained everything in great details below. See the solution below.

Q: Select all of the following tables which represent y as a function of x. Y Y Y Y -5 -4 2 2 9 13 X -4…

A: To select all the tables that represent  as a function .(1) 451215971413(2) 043252791613(3)…

Q: The function h is the reverse process of f. a. Fill in the following table to represent the…

A: NOTE: Refresh your page if you can't see any equations. . the function h subtracts 5 from each value…

Q: ƒ(x) = x³ + ac + (ab+c)x+ (a+b)x²

A:

Q: Let A = {a, b, c, d} and f = { (a, 0), (c, 12), (d, 18), (b, 12) }. Is f a function from A to B ?…

A: Given, A = {a,b,c,d} f = {(a,0) , (c,12) , (d,18) , (b,12)}

Q: Say whether the following function is injective, surjective, bijective, or none of the above (note:…

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Q: 5. Let D = {1, 2, 3, 4, 5}, C = {a, b, c, d}, and g = {(1,a), (2,c), (3,d), (4,c)}. Determine…

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Q: a. For each of the following inputs, find the corresponding output: (1,9), (7,3), (3,7), (√5.√5).…

A:

Q: Use the table shown below to answer the following questions. 1 2 3 f(x) 3 1 3 7 (a) Select the true…

A: (a) The second option is the correct option. f0=f2=3For x=0 and x=2, fx has same output.Hence, f is…

Q: On a string of pearls, the largest pearl is in the center and the smallest pearls are on the ends.…

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Q: y -1 -1 1 1 1 1 -2 -1 -3 4 -14 -5 y -1 y -1 1 1 1 1 -2 3 -6 3 -1 4 -14 4 -2 234 N/7

A:

Q: The following table gives the cost, C(n)C(n), of producing a certain good as a linear function of…

A: Given query is to find cost function using the table provided.

Q: Suppose f(x) = 3x2 + a + 6. Compute the following= A.) f( – 3) + f(2) = B.) f( – 3) – f(2) =

A: The given function is: f(x)=-3x2+x+6