2. Inverse, Exponential and Logarithmic Functions
Chapter 11
Inverse, Exponential
and
Logarithmic Functions

3. 11.1
Inverse Functions

4. Find the equation of the inverse of a function.
11.1 Inverse Functions
Objectives
Decide whether a function is one-to-one and, if it is, find its inverse.
Use the horizontal line test to determine whether a function is one-to-one.
Find the equation of the inverse of a function.
Graph f –1 from the graph of f.
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5. 11.1 Inverse Functions Functions Revisited 5 8 –3 11 2 1 3 1 2 –1 3 42 1 3
Domain
Range 1 2 –1 3 4
Domain
Range
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6. 11.1 Inverse Functions Functions Revisited 5 1 –3 8 3 11 2
Domain
Range 5 1 –3 8 3 11 2
This is a function.
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7. 11.1 Inverse Functions Functions Revisited 1 3 2 4 –1
Domain
Range 1 3 2 4 –1
This is not a function.
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8. 11.1 Inverse Functions One-to-One Functions 5 1 3 1 –3 2 8 3 4 11 2 –1
Domain
Range
Domain
Range 5 1 3 1 –3 2 8 3 4 11 2 –1
is one-to-one
is not one-to-one
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9. Relationship Between One-to-One and Inverse
11.1 Inverse Functions
Relationship Between One-to-One and Inverse .
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10. Relationship Between One-to-One and Inverse
11.1 Inverse Functions
Relationship Between One-to-One and Inverse .
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11. Horizontal Line Test and One-to-One Functions
11.1 Inverse Functions
Horizontal Line Test and One-to-One Functions .
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12. Horizontal Line Test and One-to-One Functions
11.1 Inverse Functions
Horizontal Line Test and One-to-One Functions .
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13. Finding the Equation of the Inverse of a Function
11.1 Inverse Functions
Finding the Equation of the Inverse of a Function
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14. Finding the Equation of the Inverse of a Function
11.1 Inverse Functions
Finding the Equation of the Inverse of a Function
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15. Finding the Equation of the Inverse of a Function
11.1 Inverse Functions
Finding the Equation of the Inverse of a Function
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16. Finding the Equation of the Inverse of a Function
11.1 Inverse Functions
Finding the Equation of the Inverse of a Function
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17. Finding the Equation of the Inverse of a Function
11.1 Inverse Functions
Finding the Equation of the Inverse of a Function
Solve for y.
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18. Graphing f –1 from the Graph of f
11.1 Inverse Functions
Graphing f –1 from the Graph of f
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19. Graphing f –1 from the Graph of f
11.1 Inverse Functions
Graphing f –1 from the Graph of f
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20. Graphing f –1 from the Graph of f
11.1 Inverse Functions
Graphing f –1 from the Graph of f
These pairs of points are mirror images with respect to y = x.
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