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This printable supports Common Core Mathematics Standard HSF-BF.B.4, HSF-BF.B.4c

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Finding Inverse Function Values from Tables (Grade 10)

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Finding Inverse Function Values from Tables

1. 
Some of the values of [math]f(x)[/math], an invertible function, are given in the following table. What is the value of [math]f^{-1}(1) ?[/math]

[math] \ \ \ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \ \ \ [/math][math] \ \ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \ \ [/math]
[math] 1 [/math][math] 8.9 [/math]
[math] 2 [/math][math] 5.3 [/math]
[math] 3 [/math][math] 3 [/math]
[math] 4 [/math][math] 1 [/math]
[math] 5 [/math][math] -7.5 [/math]
  1. 8.9
  2. 1
  3. -7.5
  4. 4
 
2. 
Find the value of [math]f^{-1}(-5.5)[/math], given the values of [math]f(x)[/math] in the following table. Assume that [math]f(x)[/math] has an inverse.

[math] \ \ \ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \ \ \ [/math][math] \ \ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \ \ [/math]
[math] -6 [/math][math] -20.5 [/math]
[math] -5.5 [/math][math] -11.5 [/math]
[math] -5 [/math][math] -5.5 [/math]
[math] -4.5 [/math][math] -3.5 [/math]
[math] -4 [/math][math] -1.5 [/math]
  1. -5
  2. -11.5
  3. -3.5
  4. -5.5
3. 
The following table gives some of the values of [math]f(x)[/math], a function which has an inverse. Using this information, find [math]f^{-1}(-4)[/math].


[math] \ \ \ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \ \ \ [/math][math] \ \ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \ \ [/math]
[math] -6 [/math][math] 8 [/math]
[math] -5 [/math][math] 4 [/math]
[math] -4 [/math][math] 0 [/math]
[math] -3 [/math][math] -4 [/math]
[math] -2 [/math][math] -8 [/math]
  1. -4
  2. 0
  3. -3
  4. -5
 
4. 
What is the value of [math]f^{-1}(6)[/math], given the following table? Assume that [math]f(x)[/math] has an inverse.

[math] \ \ \ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \ \ \ [/math][math] \ \ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \ \ [/math]
[math] 1/36 [/math][math] 6 [/math]
[math] 1/6 [/math][math] 10 [/math]
[math] 1 [/math][math] 23 [/math]
[math] 6 [/math][math] 54 [/math]
[math] 36 [/math][math] 103 [/math]
  1. [math]10[/math]
  2. [math]1/36[/math]
  3. [math]54[/math]
  4. It cannot be determined with the information given.
5. 
Determine the value of [math]f^{-1}(0.4)[/math], given the following table. Assume that [math]f(x)[/math] has an inverse.

[math] \ \ \ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \ \ \ [/math][math] \ \ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \ \ [/math]
[math] 0 [/math][math] 2.5 [/math]
[math] 0.4 [/math][math] 2 [/math]
[math] 0.8 [/math][math] 1 [/math]
[math] 1.2 [/math][math] 0.4 [/math]
[math] 1.6 [/math][math] -0.4 [/math]
  1. 1.2
  2. 2
  3. 1.6
  4. -0.4
 
6. 
For the invertible function [math]f(x)[/math], find the value of [math]f^{-1}(-2)[/math], given the following table.


[math] \ \ \ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \ \ \ [/math][math] \ \ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \ \ [/math]
[math] -2 [/math][math] 2 [/math]
[math] -1 [/math][math] 1 [/math]
[math] 0 [/math][math] 0 [/math]
[math] 1 [/math][math] -1 [/math]
[math] 2 [/math][math] -2 [/math]
  1. 2
  2. 1
  3. 0
  4. -2
7. 
Using the following table, what is the value of [math]f^{-1}(-1/4)[/math], given that [math]f(x)[/math] has an inverse?


[math] \ \ \ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \ \ \ [/math][math] \ \ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \ \ [/math]
[math] -4 [/math][math] 1 [/math]
[math] -1 [/math][math] 1/4 [/math]
[math] 2 [/math][math] -1/2 [/math]
[math] 5 [/math][math] -5/2 [/math]
[math] 8 [/math][math] -2 [/math]
  1. [math]1[/math]
  2. [math]-1[/math]
  3. [math]1/4[/math]
  4. It cannot be determined with the information given.
 
8. 
Given that [math]f(x)[/math] is invertible, what is the value of [math]f^{-1}(4) ?[/math] Use the following table.

[math] \ \ \ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \ \ \ [/math][math] \ \ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \ \ [/math]
[math] 0 [/math][math] -5 [/math]
[math] 2 [/math][math] -4 [/math]
[math] 4 [/math][math] 2 [/math]
[math] 6 [/math][math] 4 [/math]
[math] 8 [/math][math] 8 [/math]
  1. -4
  2. 2
  3. 4
  4. 6
9. 
If [math]f(x)[/math] is an invertible function, some of whose values are in the following table, what is the value of [math]f^{-1}(0) ?[/math]

[math] \ \ \ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \ \ \ [/math][math] \ \ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \ \ [/math]
[math] -1 [/math][math] -10 [/math]
[math] -0.5 [/math][math] -4 [/math]
[math] 0 [/math][math] -2 [/math]
[math] 0.5 [/math][math] 0 [/math]
[math] 1 [/math][math] 0.5 [/math]
  1. 1
  2. 0
  3. 0.5
  4. -2
 
10. 
The table gives some of the values of [math]f(x)[/math], an invertible function. What is the value of [math]f^{-1}(f(2)) ?[/math]

[math] \ \ \ \ \ \ \ \ \ \ \ mathbf{x} \ \ \ \ \ \ \ \ \ \ \ [/math][math] \ \ \ \ \ \ \ \ \ \ \mathbf{f(x)} \ \ \ \ \ \ \ \ \ \ [/math]
[math] -1 [/math][math] 3 [/math]
[math] -1/2 [/math][math] 2 [/math]
[math] 0 [/math][math] 1 [/math]
[math] 1/2 [/math][math] 1/2 [/math]
[math] 1 [/math][math] 1/4 [/math]
  1. [math]-1/2[/math]
  2. [math]1/2[/math]
  3. [math]2[/math]
  4. It cannot be determined with the information given.

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