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

1 Answer
Oct 31, 2015

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}