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

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Answer 1 · 2015-10-31T14:19:49

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}