Finding the domain of this function

[nothingsus]

Homework Statement

Find the domain of 1/(sqrt(2x)-1)²
Note: the minus one is not included under the square root

Homework Equations

Title

The Attempt at a Solution

So the denominator cannot be zero

so that means that sqrt(2x) cannot equal 1
x cannot be 1/2

letting the denominator be greater than 0 gets me x is greater than 1/2

my calculator says x is equal to or greater than 0 but cannot be 1/2

Where did the equal to greater than 0 part come from?

 

[Mark44]

Homework Statement

Find the domain of 1/(sqrt(2x)-1)²
Note: the minus one is not included under the square root

Homework Equations

Title

The Attempt at a Solution

So the denominator cannot be zero

so that means that sqrt(2x) cannot equal 1
x cannot be 1/2

letting the denominator be greater than 0 gets me x is greater than 1/2

my calculator says x is equal to or greater than 0 but cannot be 1/2

Where did the equal to greater than 0 part come from?

From the square root. The argument of a square root can't be negative, so you need 2x ≥ 0.

 

[SammyS]

...

letting the denominator be greater than 0 gets me x is greater than 1/2
...

Why are you concerned about the denominator being greater than zero?

 

[csleong]

The simplest way is, with the answer provided, plug in x=-1 and x=1/2 and you should know why.