Practice One-to-One Mapping in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Worksheet PDF Free Answer-key PDF Family

Quick Recap

A one-to-one (injective) function maps every distinct input to a distinct output — no two different inputs produce the same output.

No two inputs share the same output—like social security numbers.

Showing a random 20 of 50 problems.

Example 1

medium

Determine whether the floor function

f(x) = \lfloor x \rfloor

is one-to-one on

\mathbb{R}

Example 2

challenge

Find all real

b

such that

f(x) = x^3 + bx

is one-to-one on

\mathbb{R}

Example 3

medium

Is the map 'day of week to its number

1..7

' one-to-one?

Example 4

medium

f(x)=\frac{1}{x}

(for

x\neq0

) one-to-one?

Example 5

easy

Apply the horizontal line test: a line

y=2x

. Is it one-to-one?

Example 6

medium

Suppose

f

and

g

are both one-to-one. Is

f \circ g

one-to-one?

Example 7

challenge

Let

f:\mathbb{N} \to \mathbb{N}

be one-to-one. Must its image be all of

\mathbb{N}

Example 8

easy

Is the function given by the table

\{(1,4),(2,7),(3,4),(4,9)\}

one-to-one?

Example 9

hard

Find the inverse of

h(x) = \dfrac{2x+1}{x-3}

and state its domain.

Example 10

easy

Which function is NOT one-to-one? (A)

f(x)=2x-1

(B)

f(x)=x^4

\mathbb{R}

(C)

f(x)=x^5

Example 11

medium

Restrict the domain of

f(x)=x^2

to make it one-to-one. Give a valid restriction.

Example 12

medium

Show that

g(x) = x^3

is one-to-one on

\mathbb{R}

, then find its inverse function.

Example 13

easy

f(x)=3x-1

one-to-one?

Example 14

medium

f(x) = 2^x

one-to-one?

Example 15

easy

f(x) = 7x

one-to-one on

\mathbb{R}

Example 16

challenge

Let

f:\mathbb{R} \to \mathbb{R}

satisfy

f(f(x)) = x

for all

x

. Must

f

be one-to-one?

Example 17

easy

Fill in: A function is one-to-one if and only if every horizontal line meets its graph at most ____ time(s).

Example 18

hard

Find the inverse of

f(x) = \dfrac{x+2}{x-1}

and state its domain.

Example 19

challenge

f(x)=x^2-4x+7

one-to-one on the reals? Find the largest interval

[a,\infty)

where it is.

Example 20

easy

A constant function

f(x)=7

. Is it one-to-one?

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Related Concepts

Function Inverse Function Horizontal Line Test