Worksheet: Bijective (One-to-One) Functions

In this worksheet, we will practice identifying one-to-one functions.

Q1:

Which curve among those shown in the graph below is a one-to-one function?

  • Athe red one
  • Bthe orange one
  • Cthe green one
  • Dthe blue one

Q2:

Which of the following functions is one-to-one and onto from to ?

  • A 𝑓 ( 𝑥 ) = 2 𝑥 1
  • B 𝑓 ( 𝑥 ) = 1 𝑥
  • C 𝑓 ( 𝑥 ) = 3 𝑥 7
  • D 𝑓 ( 𝑥 ) = 𝑒

Q3:

Which of the following is true about a one-to-one function?

  • A It is always increasing or decreasing.
  • B It does not have an inverse.
  • C It is its own inverse.
  • D It has an inverse.

Q4:

Let 𝑓 : be given by 𝑓 ( 𝑛 ) = 𝑛 1 . What is true about 𝑓 ?

  • A 𝑓 is a bijection.
  • B 𝑓 is onto.
  • C 𝑓 is not defined.
  • D 𝑓 is one-to-one.

Q5:

Is the function shown in the graph a one-to-one function?

  • Ayes
  • Bno

Q6:

Is the function shown in the graph a one-to-one function?

  • Ano
  • Byes

Q7:

Is the function shown in the graph a one-to-one function?

  • Ano
  • Byes

Q8:

Is the function shown in the graph a one-to-one function?

  • Ayes
  • Bno

Q9:

Which of the following is a one-to-one function?

  • A 𝑓 ( 𝑥 ) = 𝑥
  • B 𝑓 ( 𝑥 ) = 𝑥 c o s
  • C 𝑓 ( 𝑥 ) = 𝑥
  • D 𝑓 ( 𝑥 ) = 𝑥 + 𝑥

Q10:

Which of the following is a one-to-one function?

  • A 𝑓 ( 𝑥 ) = 𝑥 + 2
  • B 𝑓 ( 𝑥 ) = | 𝑥 |
  • C 𝑓 ( 𝑥 ) = 𝑥
  • D 𝑓 ( 𝑥 ) = 5

Q11:

Which of the following is a bijection from to ?

  • A 𝑓 ( 𝑥 ) = 2 𝑥 1
  • B 𝑓 ( 𝑥 ) = 2 𝑥
  • C 𝑓 ( 𝑥 ) = 1 𝑥
  • D 𝑓 ( 𝑥 ) = 𝑒

Q12:

Which of the following is true about 𝑓 : ?

  • A 𝑓 cannot be onto.
  • B 𝑓 can be a bijection.
  • CImage of 𝑓 = .
  • D 𝑓 cannot be one-to-one.

Q13:

Suppose 𝑓 : given by 𝑓 𝑝 𝑞 = 𝑝 . What is the most that can be said about 𝑓 ?

  • A 𝑓 is onto
  • B 𝑓 is well-defined
  • C 𝑓 is one-to-one
  • D 𝑓 has an inverse

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