QuestionFind the domain of the function: $f(x) - 2 = x^3 - 4$ .

Studdy Solution

STEP 1

Assumptions1. The function is given as $f(x)-=x^{3}-4$ . We are asked to find the domain of the function3. The domain of a function is the set of all possible input values (often the "x" variable), which will produce a valid output from a particular function.

STEP 2

The function given is a cubic function. The domain of a cubic function is all real numbers because there are no restrictions on the input values for x.

STEP 3

The function can be rewritten as $f(x) = x^{3}-+2$ or $f(x) = x^{3}-2$ .

STEP 4

We can see that there are no square roots, logarithms, or fractions with x in the denominator that could restrict the domain. Therefore, the domain of the function is all real numbers.

STEP 5

In mathematical notation, the domain can be written as $(-\infty, \infty)$ or $R$ , which represents all real numbers.
The domain of the function $f(x) = x^{3}-2$ is all real numbers.

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