Answers:
- f(-1) = -1
- f(4) = 64
- Domain = set of all real numbers, which in interval notation is [tex](-\infty, \infty)[/tex]
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Explanation:
Replace every x with -1 and simplify
f(x) = x^3
f(-1) = (-1)^3
f(-1) = (-1)*(-1)*(-1)
f(-1) = -1
Similar steps will show that f(4) = 64
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The domain is the set of all real numbers because we can replace x with any number we want to get some result for f(x). We don't run into a division by zero error for instance, and we also don't have to worry about things like negative numbers under a square root.
The set of all real numbers can be thought of having x between negative infinity and infinity as this compound inequality [tex]-\infty < x < \infty[/tex] which condenses to the interval notation [tex](-\infty, \infty)[/tex]
The set builder notation of the domain would look something like this: [tex]\{x|x \in \mathbb{R}\}[/tex] which translates to "the set of all x values in the real number set", aka "the set of all real numbers".
If you were to graph y = x^3, you would find it stretches forever to the left and to the right. This visually shows that the domain is the set of all real numbers.
