What are the domain and range of f(x) = log(x-1)+2?

Find the Domain and Range f(x) = log of x-1+2

f

(

x

)

=

log

(

x

−

1

)

+

2

f(x)=log(x-1)+2

Set the argument in

log

(

x

−

1

)

log(x-1) greater than

0

0 to find where the expression is defined.

x

−

1

>

0

x-1>0

Add

1

1 to both sides of the inequality.

x

>

1

x>1

The domain is all values of

x

x that make the expression defined.

Interval Notation:

(

1

,

∞

)

(1,∞)

Set-Builder Notation:

{

x

|

x

>

1

}

{x|x>1}

The range is the set of all valid

y

y values. Use the graph to find the range.

Interval Notation:

(

−

∞

,

∞

)

(-∞,∞)

Set-Builder Notation:

{

y

|

y

∈

R

}

{y|y∈ℝ}

Determine the domain and range.

Domain:

(

1

,

∞

)

,

{

x

|

x

>

1

}

(1,∞),{x|x>1}

Range:

(

−

∞

,

∞

)

,

{

y

|

y

∈

R

}

(-∞,∞),{y|y∈ℝ}

answer: the answer is e

step-by-step explanation: