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Chapter 2: Q64E (page 155)

Draw the graph of the function f (x) = [x/2] from R to R.

Short Answer

Expert verified

Given f (x) = [x/2]

Draw the graph of the given function using the graphing tool, we get,

Step by step solution

01

Step: 1

Given f (x) = [x/2]

Draw the graph of the given function using the graphing tool, we get,

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Most popular questions from this chapter

Specify a codomain for each of the functions in Exercise 17. Under what conditions is each of the functions with the codomain you specified onto?

Prove or disprove each of these statements about the floor and ceiling functions.

  1. [⌊x⌋⌉=⌊x⌋for all real numbers x.
  2. ⌊2x⌋=2⌊x⌋whenever x is a real number.
  3. ⌈x⌉+⌈y⌉−⌈x+y⌉=0or1whenever x and y are real numbers.
  4. ⌈xy⌉=⌈x⌉⌈y⌉for all real numbers x and y.
  5. x2=x+12for all real numbers x.

Suppose that g is a function from A to B and f is a function from B to C.

  1. Show that if both f and g are one-to-one functions, thenf∘gis also one-to-one.
  2. Show that if both f and g are onto functions, then f∘g is also onto.

Determine whether each of these functions is a bijection from R to R.

  1. fx=2x+1
  2. fx=x2+1
  3. fx=x
  4. fx=x2+1/x2+2

Question: Find f∘gand g∘f, wheref(x)=x2+1 and g(x)=x+2, are functions from ℝtoℝ.
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