QuestionFind $f(x)$ for $x=-1,4$ and determine the domain of $f$ , where $f(x)=x^{3}$ .

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=x^{3}$ . The values of $x$ we need to find $f(x)$ for are $x=-1$ and $x=4$

STEP 2

We can find $f(x)$ for the given values of $x$ by substituting the values of $x$ into the function.
For $x=-1$ $f(-1)=(-1)^{}$

STEP 3

Calculate the value of $f(-1)$ .
$f(-1)=(-1)^{3}=-1$

STEP 4

Now, let's find $f(x)$ for $x=4$ .
$f(4)=(4)^{3}$

STEP 5

Calculate the value of $f(4)$ .
$f(4)=(4)^{3}=64$

STEP 6

The domain of a function $f$ is the set of all real numbers $x$ for which the function $f(x)$ is defined.For the function $f(x)=x^{3}$ , it is defined for all real numbers. Therefore, the domain of $f$ is all real numbers.
We can write this in interval notation as $(-\infty, \infty)$ So, the answers are(a) $f(-1)=-1$ and $f(4)=64$ (b) The domain of $f$ is $(-\infty, \infty)$

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