• Given any function, f, the inverse of

the function, f -1, is a relation that is

formed by interchanging each (x, y)

of f to a (y, x) of f -1. 

Let f be defined as the set of values given by

x-values -2 0 4 7

y-values 0 4 -5 10

Let f -1 be defined as the set of values given by

x-values 0 4 -5 10

y-values -2 0 4 7

x y

-2 13

0 7

4 -5

7 -14

Function 1

Function 2

x y

13 -2

7 0

-5 4

-14 7

–6 –4 –2 2 4 6

–6

–4

–2

2

4

6

x

y

y = x

Let

To find the inverse, switch x and y,

Solve for y:

35 x

xy

35 y

yx

yyx )35(yxxy 35xyxy 35

xxy 315

15

3

x

xy

So the inverse of 35

:)(

x

xyxf is

15

3:)(1

x

xyxf

42 xy 1. Exchange x and y

2. Solve for y.

3. Graph both lines.

4. Graph

5. What does this line represent?

42 yx42 xy2

2

1 xy

xy

−6 −4 −2 2 4 6

−6

−4

−2

2

4

6

x

y

Equation 2: y=.5x+2

Equation 1: y=2x−4

42 2 xy1. Exchange x and y

2. Solve for y.

3. Graph both curves.

4. Graph

5. What does this line represent?

42 2 yx42 2 xy

22

12 xy

xy

22

1 xy

−10 −5 5

−6

−4

−2

2

4

6

x

y

xy 2 1. Exchange x and y

2. Solve for y.yx 2

In this case y is the exponent. How could we solve for y. Mathematicians had to come up with a new term to represent the solution of this equation.

xy 2log−10 −5 5

−6

−4

−2

2

4

6

x

y

xy 2

xy 2log

Rewrite the following Exponential Equations into Logarithmic Equations

EXAMPLE 1

823 38log2 Base

Exponent

Power (Argument)

Power (Argument)

Base Exponent

Rewrite the following Exponential Equations into Logarithmic Equations

EXAMPLE 2

1000

110 3 3

1000

1log10

Base

Exponent

Power (Argument)

Power (Argument)

Base Exponent

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EXAMPLE 3

532log2

Base Exponent

Power (Argument)

Power (Argument)

BaseExponent

3225

Rewrite the following Logarithmic Equations into Exponential Equations

EXAMPLE 4

327log3

Base Exponent

Power (Argument)

Power (Argument)

BaseExponent

2733