Question 153044: In interval notation, what is the domain of f(x) = 2x^3 – 4x – 7?
@ f(x) is a cubic, so there are no restrictions on its domain. Answer (a) is in the wrong form for use of infinity as interval limits.
a. x ∈ [-∞, ∞]
b. x ∈ (-∞, ∞)
c. f(x) ∈ [-7, ∞)
d. The range cannot be determined
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Looking at  , we can see that there are no square roots, logs, and other functions where there are restrictions on the domain.
Also, we can see that the function does not have a division by x (or any combination of variables and constants).
So we don't have to worry about division by zero.
Since we don't have any restrictions on the domain, this shows us that the domain is all real numbers. In other words, we can plug in any number in for x
So the domain of the function in set-builder notation is:
In plain English, this reads: x is the set of all real numbers (In other words, x can be any number)
Also, in interval notation, the domain is:
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