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what is the inverse of f(×) =-2×-8?​

Sagot :

Srspc21iglesiajellsyidn

Algebra Examples

Popular Problems Algebra Find the Inverse Function f(x)=8x-2

f

(

x

)

=

8

x

−

2

Replace

f

(

x

)

with

y

.

y

=

8

x

−

2

Interchange the variables.

x

=

8

y

−

2

Solve for

y

.

y

=

x

8

+

1

4

Solve for

y

and replace with

f

−

1

(

x

)

.

f

−

1

(

x

)

=

x

8

+

1

4

Symelvillejeanidn

Answer:

The inverse of f(x)=x2−2x−8 is

XXX¯f(x)=1±√x+9

which is not a function since it generates multiple solution values.

Explanation:

If ¯f(x) is the inverse of f(x)

then f(¯f(x))=x (by definition of inverse)

Therefore

(¯f(x))2−2⋅(¯f(x))−8=x

¯f(x)2−2¯f(x)+1=x+8+1

(¯f(x)−1)2=x+9

¯f(x)−1=±√x+9

¯f(x)=1±√x+9