Identifying the domain of a function

Question

Using interval function, find the domain of f(x)=1/5x^3-4

 

The answer key says (negative infinity, positive infinity), but I don't know how to arrive at the answer. 

Answer 1

Ignore the other numbers for now; the only important part is our variable x. What's happening is that we take x and cube it, or x * x * x.

this means  it is, say, at x = 100, then f(x) = 100 * 100 * 100, or f(x) = 1,000,000.

Now say we put in -100, then f(x) = -100 * -100 * -100, or  f(x) = -1,000,000.

Remember, a negative * negative = positive.

Negative * positive = Negative.

So Neg * Neg * Neg  -->  Pos * Neg  -->  Neg number

 

The 1/5 will slow it down, but it won't stop the growth. Taking 4 away is just a joke when we hit numbers that high.