Inverse of f (x) = 4x-6

f

(

x

)

=

4

x

-

6

Replace

f

(

x

)

with

y

.

y

=

4

x

-

6

Interchange the variables.

x

=

4

y

-

6

Solve for

y

.

Rewrite the equation as

4

y

-

6

=

x

.

4

y

-

6

=

x

Add

6

to both sides of the equation.

4

y

=

x

+

6

Divide each term by

4

and simplify.

y

=

x

4

+

3

2

Solve for

y

and replace with

f

-

1

(

x

)

.

Replace the

y

with

f

-

1

(

x

)

to show the final answer.

f

-

1

(

x

)

=

x

4

+

3

2

Set up the composite result function.

g

(

f

(

x

)

)

Evaluate

g

(

f

(

x

)

)

by substituting in the value of

f

into

g

.

4

x

-

6

4

+

3

2

Simplify terms.

g

(

4

x

-

6

)

=

2

x

-

3

+

3

2

Simplify the numerator.

g

(

4

x

-

6

)

=

2

x

2

Cancel the common factor of

2

.

g

(

4

x

-

6

)

=

x

Since

g

(

f

(

x

)

)

=

x

,

f

-

1

(

x

)

=

x

4

+

3

2

is the inverse of

f

(

x

)

=

4

x

-

6

.

f

-

1

(

x

)

=

x

4

+

3

2