Lesson Worksheet: Injective Functions Mathematics

In this worksheet, we will practice determining whether a function is a one-to-one function (injective).

Q1:

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

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

Q2:

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

  • A𝑓(𝑥)=𝑥
  • B𝑓(𝑥)=𝑥+2
  • C𝑓(𝑥)=|𝑥|
  • D𝑓(𝑥)=5

Q3:

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

  • A𝑓(𝑥)=𝑥cos
  • B𝑓(𝑥)=𝑥
  • C𝑓(𝑥)=𝑥
  • D𝑓(𝑥)=𝑥+𝑥

Q4:

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

  • ANo
  • BYes

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?

  • AYes
  • BNo

Q7:

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

  • AYes
  • BNo

Q8:

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

  • AIt does not have an inverse.
  • BIt is always increasing or decreasing.
  • CIt has an inverse.
  • DIt is its own inverse.

Q9:

Let 𝑓: be given by 𝑓(𝑛)=𝑛1. What is true about 𝑓?

  • A𝑓 is a bijection.
  • B𝑓 is not defined.
  • C𝑓 is onto.
  • D𝑓 is one-to-one.

Q10:

Determine whether 𝑓(𝑥)=𝑥sin is a one-to-one function in each of the following cases.

Case 1: 𝑥

  • AYes
  • BNo

Case 2: 𝑥𝜋2,𝜋2

  • ANo
  • BYes

This lesson includes 27 additional questions and 154 additional question variations for subscribers.

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