Find the domain of the following function. y = x 3 − 2 x + 1 y=x^3-2x+1

Asks us to find the domain of the following function. So how do we go about doing this? Well, I can see that we have y equals x cubed minus two x plus one. Now, when it comes to domain restrictions, there are a couple of things that come to mind. One of the thing that I know is that if we have some quantity or number and it's in a fraction, because we cannot divide by zero. But I can see nothing here is being divided, so I don't have to worry about the dividing by zero restriction, because we're not allowed to divide by zero. But what I can also know is the square root rule. We cannot take the square root of a negative number. But I can see that there aren't really any radicals or square roots happening here either. So let's keep looking to see if there are any domain restrictions. The domain would be any kind of input that we could put in here that's going to somehow break our function. Now I'm gonna try a couple of numbers here. I'm going to start with something like positive one. Now we put in positive one, this is what we get. Now one cubed is one, that's gonna be minus two times one, which is two plus one. So we get one minus two plus one, which all just comes out to zero. Well that's fine, that didn't break our function, there was nothing, no math rules that we broke here, so we're good. Let's try something different. Let's try an x value of zero. So what would be zero cubed minus two times zero plus one? Well, in this case, both of these terms would just become zero. So we just end up with zero plus one, which is just one. That's fine. No problems there. Let's now try a negative number. So we'll have y is equal to negative one cubed, replacing that x with negative one. And then we'll have minus two times negative one plus one. I'm just trying some different numbers here to see if there's any case that's going to break our function here or any inputs we're not allowed to have. In this case, negative one times negative one times negative one all just comes out to negative one. Then we have negative two times negative one, which comes out to positive two, then we have plus one, so what we end up getting is just two, and that's perfectly fine as well. If we plug in a positive, a negative, a zero, it ends up being fine, and you can actually keep trying x's, and it's going to be fine. There's not really any situation where our function here is going to break. There's no inputs that are gonna break this. And so because of that, we can say that this is gonna be all real numbers. So everything from negative infinity to positive infinity is allowed, and that right there is the domain of our function.

Find the domain of the following function.y=x3−2x+1y=$$x^3-2x+1 $$

(−∞,0]\left(-\infty,0\right\rbrack

[0,∞)\left\lbrack0,\infty\right)

(−∞,2)∪(2,∞)\left(-\infty,2\right)\cup\left(2,\infty\right)

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Find the domain of the following function.
$y = x^{3} - 2 x + 1$

$open paren negative infinity comma 0 close bracket$

$open bracket 0 comma infinity close paren$

$open paren negative infinity comma 2 close paren union open paren 2 comma infinity close paren$

$$\left$(-$\infty$,$\infty\]\right$)$

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검증된 단계별 안내

Identify the given function: $y = x^3 - 2x + 1$.

Recall that the domain of a function is the set of all real numbers $x$ for which the function is defined.

Since the function is a polynomial (a cubic polynomial), it is defined for all real numbers because polynomials do not have restrictions like division by zero or square roots of negative numbers.

Therefore, the domain includes all real numbers from negative infinity to positive infinity.

Express the domain in interval notation as $\left(-\infty, \infty\right)$.