Question

How do you find the domain of `g(x)= root3x/(x^2+x-90)`?

Answer 1

For the domain of x, you need to search the values of x for which this function becomes defined.

One thing, in this function g(x) , it is not defined when the denominator = 0.

So for what value to x does the denominator becomes 0 ?

`x^2 + x - 90 =0`

`x^2 + ( 10-9 ) -90 =0`

`x^2 + 10x - 9x -90 =0`

`x ( x+10) -9 ( x+ 10) =0`

`(x+10) ( x-9) =0`

either,

`x+10 =0`
So, `x= -10`

or,
`x-9=0`
`So, x=9`

So when the value of `x` is either 9 or -10, the denominator becomes 0 and the function g(x) becomes undefined.

Therefore, for all values of `x` except 9 and -10, the function is defined.

Domain of `x` is R ( real line ) `!=` {9,-10}