find the domain of g (x)=2/x^2-5x-24 in interval notation

Question

Determine the domain of the following function. Use interval notation.

Answer 1

If you mean g(x) = 2/(x²-5x-24), then g(x) = 2/[(x-8)(x+3)]

 

So, the denominator is equal to zero when x = 8 or -3.

 

Since division by zero is undefined, 

 

Domain = {x l x≠8,-3}

 

            = (-∞,-3)∪(-3,8)∪(8,∞)

Answer 2

The only 'difficulty' with the function is that x squared appears in a denominator. That prohibits x from being zero. Therefore the domain is all Reals except 0.

 

Otherwise, any Real number substituted into g(x) will 'output' a Real number (for the range).

 

The domain is (-infinity, 0) ∪ (0, infinity).