25.9k views
1 vote
Consider the following. f(x)=(8x^(3)-x^(2)+7)/(3x^(3)+24) (a) Find the domain of the function

User Sherman
by
9.2k points

1 Answer

4 votes

In order to find the domain of the given function, we need find for which x-values the function is defined. The issue would be if the denominator equals 0, which would make the function undefined.

So, we have to find the solutions of equation 3x^3 + 24 = 0.

To solve for x, we need to get 3x³ on its own. We do this by subtracting 24 from both sides of the equation to isolate 3x^3:

3x^3 = -24

Then we divide both sides of the equation by 3 to isolate x^3:

x^3 = -24/3

We simplify the right-hand side to get:

x^3 = -8

Now, to solve for x, we could take the cube root of both sides to get

x = -2

So the function is not defined when x = -2.

Now let's figure out the domain. The domain of the function will be all real numbers except for x = -2. In interval notation, we can represent this as (-∞, -2) U (-2, ∞). "U" denotes the union of two sets, meaning that the domain includes all numbers from negative infinity to -2, and from -2 to positive infinity, but does not include -2 itself.

So, the domain of the function is all real x, except x=-2.

User Makoto Miyazaki
by
7.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories