a) What is the domain of $$ f(x)=-24 x^{9}+37 x^{6}+31 x^{4}-6 x^{3}+38 x^{2}-16 $$ ? Answer: $$ (-\infty, \infty) $$ ount $$ \square $$ No matter what $$ x $$-value you enter, you'll get an answer back from the function. $$ \square $$ There is no solution to the problem. $$ \square $$ Any number is allowed to be used for $$ x $$. $$ \square $$ The answers are 1 and -16. $$ \square $$ There are no allowed numbers that you can use for $$ x $$.

Question

UpStudy AI · Accepted Answer

To determine the domain of the function $$ f(x) = -24 x^{9} + 37 x^{6} + 31 x^{4} - 6 x^{3} + 38 x^{2} - 16 $$, we need to analyze the function.

1. **Identify the type of function**: The function $$ f(x) $$ is a polynomial. Polynomials are defined for all real numbers.

2. **Domain of polynomial functions**: The domain of any polynomial function is all real numbers because there are no restrictions such as division by zero or square roots of negative numbers.

Thus, the domain of $$ f(x) $$ is indeed $$ (-\infty, \infty) $$.

Now, let's evaluate the provided answer options:

- $$ \square $$ No matter what $$ x $$-value you enter, you'll get an answer back from the function. (True, but not a direct answer)
- $$ \square $$ There is no solution to the problem. (False)
- $$ \square $$ Any number is allowed to be used for $$ x $$. (True, but not a direct answer)
- $$ \square $$ The answers are 1 and -16. (False, these are not relevant to the domain)
- $$ \square $$ There are no allowed numbers that you can use for $$ x $$. (False)

The correct answer is that the domain of $$ f(x) $$ is $$ (-\infty, \infty) $$.
The domain of $$ f(x) $$ is all real numbers, so $$ (-\infty, \infty) $$.

Real Tutor Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Algebra Questions