How do you find the domain of g(x) = x/((x-1)(x+3))g(x)=x(x−1)(x+3)?

1 Answer
Shura
May 12, 2015

The answer is : D = RR-{-3;1}.

The domain of a function is all the values that x can take.

Think about it this way : In a usual function, it is all the real numbers (RR) except some numbers or ranges of numbers. Basically, it is all the x you can't use because your function wouldn't give you a finite result (it would give you oo or something you can't calculate, like sqrt(-3)).

So we have : g(x) = x/((x-1)(x+3))

In your case, since we have a fraction, you know you can't divide by zero.

So you will avoid having -3 and 1 as values of x and exclude them from the domain :

D = RR-{-3;1} or

D = ]-oo;-3[ uu ]-3;1[ uu ]1; +oo[.

You got your answer.

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