Finding the domain of this function

In summary, the domain of the function 1/(sqrt(2x)-1)^2 is all real numbers except for x = 1/2. This is because the denominator cannot be equal to 0, and when solving for the range of x, it is found that x must be greater than 1/2. The concern for the denominator being greater than 0 arises from the argument of the square root, which cannot be negative.
  • #1
nothingsus
16
0

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?
 
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  • #2
nothingsus said:

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.
 
  • #3
nothingsus said:
...

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?
 
  • #4
The simplest way is, with the answer provided, plug in x=-1 and x=1/2 and you should know why.
 

FAQ: Finding the domain of this function

What is the domain of a function?

The domain of a function is the set of all possible input values for which the function is defined and produces an output.

How do you find the domain of a function?

To find the domain of a function, you need to look for any restrictions on the input values. This can include restrictions on the type of numbers allowed, such as only positive numbers, or restrictions on certain variables, such as avoiding division by zero.

What are some common restrictions that can affect the domain of a function?

Some common restrictions that can affect the domain of a function include square roots of negative numbers, division by zero, and logarithms of non-positive numbers. These restrictions may result in the function being undefined for certain input values.

Can the domain of a function change?

Yes, the domain of a function can change depending on the specific function and any restrictions on the input values. For example, the domain of a rational function may change if there are restrictions on the values that can be used in the denominator.

Why is it important to find the domain of a function?

It is important to find the domain of a function in order to ensure that the function is well-defined and to avoid any potential errors or undefined outputs. Knowing the domain can also help in understanding the behavior and characteristics of the function.

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