Reference no: EM131222069
1. Determine whether f is a Mnetion from Z to R It if
a. f(x) = ±x
b. f(n) =(n2 + 1)½.
c. f(n) = 1 / (n2 - 4)
2. Rind the domain avd range of these fractions.
a. the function ...signs b each pair of positive integers the first integer of the par
b. the function Nat assigns to each positive integer its largest decimal digit
c. the function Nat assigns to a bit string the number of ...runs the numb...zeros in the string
d. the function that assigns to each positive integer the Ingest integer not exceeding the square of the integer
e. the function that assigns to a bit string the longest string of one in the string
3. Determine whether each of these function from Z to Z is 1-1 or is an injection. Justify your answer.
a. f(n) = n-1
b. f(n) = n2 + 1
c. f(n) = n3
d. f(n) = ⌈n/2⌉
4. Determine whether f: Zx Z → Z is onto or is a surjection if
a. f(m,n) = 2m-n
b. f(m,n) = m2 - n2
c. f(m,n) = m + n + 1
d. f(m,n) = m2 - 4
5. Determine whether each of these function is a bijectin or 1-1 correspondence from R to R.
a. f(x) = -3x + 4
b. f(x) = -3x2 + 7
c. f(x) = x5 + 1
6. LelS w -1,0,2,4,7 4. Pind f ( ) if
a. f(x) = 1
b. f(x) = 2x + 1
c. f(x) = ⌈x/5⌉
d. f(x) = ⌊(x2 + 1) / 3⌋
7. Decompose the Mmition f (x)= 1 + x2 into simpler functions.
8. Draw the grapb of the function f (x) = ⌈x⌉ + ⌊x/2⌋ from R to R.
9. Suppose that f is an inertible function from Y to Z andg is an invertible function from X to Y. Show that the inverse of the composition f°g is given (f°g)-1=g-1°f-1
10. A function 1-1 on the specified domain X. By letting Y be the range of f, we obtain a bijestion from X to Y. Find the inverse function of f (x) = 6+27x-1, where Xie set of real numbers.
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