QuestionEvaluate $(f \circ f)(2)$ for $f(x)=x^{3}-4x$ . What is the exact value?

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is given by $f(x)=x^{3}-4 x$ . We are asked to evaluate the function $(f \circ f)(x)$ for $x=$

STEP 2

The composition of the function $f$ with itself, denoted as $(f \circ f)(x)$ , means applying the function $f$ twice. In other words, it means plugging the output of the function $f(x)$ back into the function $f(x)$ .
$(f \circ f)(x) = f(f(x))$

STEP 3

First, we need to find the value of $f(x)$ for $x=2$ . We can do this by substituting $x=2$ into the function $f(x)$ .
$f(2) = (2)^{3}-(2)$

STEP 4

Calculate the value of $f(2)$ .
$f(2) =8 -8 =0$

STEP 5

Now, we need to find the value of $(f \circ f)(2)$ . We can do this by substituting $f(2)$ into the function $f(x)$ .
$(f \circ f)(2) = f(f(2)) = f(0)$

STEP 6

Substitute $x=0$ into the function $f(x)$ to find the value of $f(0)$ .
$f(0) = (0)^{3}-4(0)$

STEP 7

Calculate the value of $f(0)$ .
$f(0) =0 -0 =0$ Therefore, $(f \circ f)(2)$ is $0$ .

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QuestionEvaluate $(f \circ f)(2)$ for $f(x)=x^{3}-4x$ . What is the exact value?

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is given by $f(x)=x^{3}-4 x$ . We are asked to evaluate the function $(f \circ f)(x)$ for $x=$

STEP 2

The composition of the function $f$ with itself, denoted as $(f \circ f)(x)$ , means applying the function $f$ twice. In other words, it means plugging the output of the function $f(x)$ back into the function $f(x)$ .
$(f \circ f)(x) = f(f(x))$

STEP 3

First, we need to find the value of $f(x)$ for $x=2$ . We can do this by substituting $x=2$ into the function $f(x)$ .
$f(2) = (2)^{3}-(2)$

STEP 4

Calculate the value of $f(2)$ .
$f(2) =8 -8 =0$

STEP 5

Now, we need to find the value of $(f \circ f)(2)$ . We can do this by substituting $f(2)$ into the function $f(x)$ .
$(f \circ f)(2) = f(f(2)) = f(0)$

STEP 6

Substitute $x=0$ into the function $f(x)$ to find the value of $f(0)$ .
$f(0) = (0)^{3}-4(0)$

STEP 7

Calculate the value of $f(0)$ .
$f(0) =0 -0 =0$ Therefore, $(f \circ f)(2)$ is $0$ .

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QuestionEvaluate (f∘f)(2)(f \circ f)(2)(f∘f)(2) for f(x)=x3−4xf(x)=x^{3}-4xf(x)=x3−4x. What is the exact value?

Studdy Solution

STEP 1

Assumptions1. The function f(x)f(x)f(x) is given by f(x)=x3−4xf(x)=x^{3}-4 xf(x)=x3−4x . We are asked to evaluate the function (f∘f)(x)(f \circ f)(x)(f∘f)(x) for x=x=x=

STEP 2

STEP 3

First, we need to find the value of f(x)f(x)f(x) for x=2x=2x=2. We can do this by substituting x=2x=2x=2 into the function f(x)f(x)f(x).f(2)=(2)3−(2) f(2) = (2)^{3}-(2) f(2)=(2)3−(2)

STEP 4

Calculate the value of f(2)f(2)f(2).f(2)=8−8=0 f(2) =8 -8 =0 f(2)=8−8=0

STEP 5

Now, we need to find the value of (f∘f)(2)(f \circ f)(2)(f∘f)(2). We can do this by substituting f(2)f(2)f(2) into the function f(x)f(x)f(x).(f∘f)(2)=f(f(2))=f(0) (f \circ f)(2) = f(f(2)) = f(0) (f∘f)(2)=f(f(2))=f(0)

STEP 6

Substitute x=0x=0x=0 into the function f(x)f(x)f(x) to find the value of f(0)f(0)f(0).f(0)=(0)3−4(0) f(0) = (0)^{3}-4(0) f(0)=(0)3−4(0)

STEP 7

Calculate the value of f(0)f(0)f(0).f(0)=0−0=0 f(0) =0 -0 =0 f(0)=0−0=0Therefore, (f∘f)(2)(f \circ f)(2)(f∘f)(2) is 000.

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QuestionEvaluate $(f \circ f)(2)$ for $f(x)=x^{3}-4x$ . What is the exact value?

Assumptions1. The function $f(x)$ is given by $f(x)=x^{3}-4 x$ . We are asked to evaluate the function $(f \circ f)(x)$ for $x=$

First, we need to find the value of $f(x)$ for $x=2$ . We can do this by substituting $x=2$ into the function $f(x)$ .
$f(2) = (2)^{3}-(2)$

Calculate the value of $f(2)$ .
$f(2) =8 -8 =0$

Now, we need to find the value of $(f \circ f)(2)$ . We can do this by substituting $f(2)$ into the function $f(x)$ .
$(f \circ f)(2) = f(f(2)) = f(0)$

Substitute $x=0$ into the function $f(x)$ to find the value of $f(0)$ .
$f(0) = (0)^{3}-4(0)$

Calculate the value of $f(0)$ .
$f(0) =0 -0 =0$ Therefore, $(f \circ f)(2)$ is $0$ .