Find the domain of the given function. Write your answers in both set builder and interval notation. `f(x)= (2x^2)/sqrt(4x -1)` `

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`f(x)=(2x^2)/sqrt(4x-1)`

Note that domain refers to the values of x that are allowed in a function.

Since the given function is in fraction form, to get the domain, we need to take note that in fractions zero denominator is not allowed. Also, we have to consider the properties of square...

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`f(x)=(2x^2)/sqrt(4x-1)`

Note that domain refers to the values of x that are allowed in a function.

Since the given function is in fraction form, to get the domain, we need to take note that in fractions zero denominator is not allowed.
Also, we have to consider the properties of square root. In square root, negative radicand are not allowed.

So, to determine the domain of f(x), set the radicand in the denominator greater than zero.

`4x-1gt0`

`4x-1+1gt0+1`

`4xgt1`

`(4x)/4gt1/4`

`xgt1/4`

Therefore, domain of the given function are all real numbers that are greater than `1/4` . Its set builder notation is `{x|xepsilonR, xgt1/4}` . And its interval notation is `(1/4,oo)` .

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