Find the domain of the given function. Write your answers in both set builder and interval notation, also with absolute value. : f(x)= 2x`/` `sqrt(6x^2 -1)`

aruv | Student

Find the domain of the given function.


Assume f is real function.

function f is defined if `sqrt(6x^2-1)!=0`

also f is real therefore






`-1/sqrt(6)>x and x>1/sqrt(6)`

Thus domain of the function f is


In set builder notation

`D={x: x<-1/sqrt(6) and x>1/sqrt(6),x inRR}`

llltkl | Student

For radical functions of even index defined over real numbers, the domain is the set of possible values. These values must be non-negative.

Again, there is a restriction of division by zero.

Hence `6x^2-1gt0`




So, the domain of `(2x)/(sqrt6x^2-1)` is:

`{x|x in RR, xgtsqrt(1/6)}` orĀ  ` [sqrt(1/6),oo)` .