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

Studdy Solution

STEP 1

Assumptions1. The function is defined as $f(x)=x^{3}$ . We need to find the values of $f(x)$ for $x=-1$ and $x=4$
3. We also need to find the domain of $f$

STEP 2

First, let's find the value of $f(x)$ for $x=-1$ . We can do this by substituting $x=-1$ into the function.
$f(-1)=(-1)^{}$

STEP 3

Calculate the value of $f(-1)$ .
$f(-1)=(-1)^{3}=-1$ So, the correct choice is A. $f(-1)=-1$

STEP 4

Next, let's find the value of $f(x)$ for $x=4$ . We can do this by substituting $x=4$ into the function.
$f(4)=(4)^{3}$

STEP 5

Calculate the value of $f(4)$ .
$f(4)=(4)^{3}=64$ So, the correct choice for $f(4)$ is $64$ .

STEP 6

Now, let's find the domain of $f$ . The domain of a function is the set of all possible input values (x-values) which will produce a valid output.
For the function $f(x)=x^{3}$ , there are no restrictions on the values that $x$ can take. This is because any real number can be cubed.
So, the domain of $f$ is all real numbers, which can be written in interval notation as $(-\infty, \infty)$ .

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

Studdy Solution

STEP 1

Assumptions1. The function is defined as $f(x)=x^{3}$ . We need to find the values of $f(x)$ for $x=-1$ and $x=4$
3. We also need to find the domain of $f$

STEP 2

First, let's find the value of $f(x)$ for $x=-1$ . We can do this by substituting $x=-1$ into the function.
$f(-1)=(-1)^{}$

STEP 3

Calculate the value of $f(-1)$ .
$f(-1)=(-1)^{3}=-1$ So, the correct choice is A. $f(-1)=-1$

STEP 4

Next, let's find the value of $f(x)$ for $x=4$ . We can do this by substituting $x=4$ into the function.
$f(4)=(4)^{3}$

STEP 5

Calculate the value of $f(4)$ .
$f(4)=(4)^{3}=64$ So, the correct choice for $f(4)$ is $64$ .

STEP 6

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QuestionFind f(x)f(x)f(x) for x=−1x=-1x=−1 and x=4x=4x=4 if f(x)=x3f(x)=x^{3}f(x)=x3. Also, determine the domain of fff.

Studdy Solution

STEP 1

Assumptions1. The function is defined as f(x)=x3f(x)=x^{3}f(x)=x3 . We need to find the values of f(x)f(x)f(x) for x=−1x=-1x=−1 and x=4x=4x=43. We also need to find the domain of fff

STEP 2

First, let's find the value of f(x)f(x)f(x) for x=−1x=-1x=−1. We can do this by substituting x=−1x=-1x=−1 into the function.f(−1)=(−1)f(-1)=(-1)^{}f(−1)=(−1)

STEP 3

Calculate the value of f(−1)f(-1)f(−1).f(−1)=(−1)3=−1f(-1)=(-1)^{3}=-1f(−1)=(−1)3=−1So, the correct choice is A. f(−1)=−1f(-1)=-1f(−1)=−1

STEP 4

Next, let's find the value of f(x)f(x)f(x) for x=4x=4x=4. We can do this by substituting x=4x=4x=4 into the function.f(4)=(4)3f(4)=(4)^{3}f(4)=(4)3

STEP 5

Calculate the value of f(4)f(4)f(4).f(4)=(4)3=64f(4)=(4)^{3}=64f(4)=(4)3=64So, the correct choice for f(4)f(4)f(4) is 646464.

STEP 6

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

Assumptions1. The function is defined as $f(x)=x^{3}$ . We need to find the values of $f(x)$ for $x=-1$ and $x=4$
3. We also need to find the domain of $f$

First, let's find the value of $f(x)$ for $x=-1$ . We can do this by substituting $x=-1$ into the function.
$f(-1)=(-1)^{}$

Calculate the value of $f(-1)$ .
$f(-1)=(-1)^{3}=-1$ So, the correct choice is A. $f(-1)=-1$

Next, let's find the value of $f(x)$ for $x=4$ . We can do this by substituting $x=4$ into the function.
$f(4)=(4)^{3}$

Calculate the value of $f(4)$ .
$f(4)=(4)^{3}=64$ So, the correct choice for $f(4)$ is $64$ .