Question

find the domain and range of the real function f denoted by f(x)=
$\sqrt{x - 1}$



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Answer 1

Answer:

x ∈ [ 1 , ∞ )

y ∈ [ 0 , ∞ )

Step-by-step explanation:

Given :

f ( x ) = √ ( x - 1 )

Domain :

= >  √ ( x - 1 ) ≥ 0

= > x - 1 ≥ 0

= > x ≥ 1

x ∈ [ 1 , ∞ )

Range :

Let y = √ ( x - 1 )

= > x - 1 = y²

= > x = y² + 1

= > y² ≥ 0

y ∈ [ 0 , ∞ )

Hence we get required answer!

Answer 2

QUESTION:

Find the domain and range of the real function f denoted by f(x) = √x - 1

GIVEN:

• f(x) = √x - 1

TO FIND:

• Domain
• Range

SOLUTION:

Firstly finding the Domain

f(x) = √x - 1

Seperate the function into two parts

√x - 1

x - 1

Find all values for which the radicand is positive or 0 Domain is all real numbers

x ≥ 1

x belongs to R

Where R is real numbers

Find the union

x belongs to [1 , ∞)

Alternative form

x ≥ 1

Now, finding the range

Let

y = √x - 1

→ y² = x - 1

→ y² + 1 = x

→ y² ≥ 0

Now,

y belongs to [0 , ∞)

Refer the attachment