QuestionFind the function $(g \circ f \circ h)(x)$ for $f(x)=4x-6$ , $g(x)=x^3$ , and $h(x)=\sqrt[4]{x}$ .

Studdy Solution

STEP 1

Assumptions1. The function $f(x)=4x-6$ . The function $g(x)=x^{3}$
3. The function $h(x)=\sqrt[4]{x}$
4. We are asked to find the composition of functions $(g \circ f \circ h)(x)$

STEP 2

The composition of functions is a concept in mathematics where the output of one function becomes the input of another function. In other words, the output of the function $h(x)$ will be the input for the function $f(x)$ , and the output of $f(x)$ will be the input for $g(x)$ .

STEP 3

First, we need to find the output of $h(x)$ , which is $\sqrt[]{x}$ .

STEP 4

Next, we substitute the output of $h(x)$ into $f(x)$ , which is $4x-6$ . This gives us $f(h(x))$ .
$f(h(x)) =4h(x) -6$

STEP 5

Substitute the value of $h(x)$ into the equation.
$f(h(x)) =4\sqrt[4]{x} -$

STEP 6

Now, we substitute $f(h(x))$ into $g(x)$ , which is $x^{3}$ . This gives us $g(f(h(x)))$ .
$g(f(h(x))) = (f(h(x)))^{3}$

STEP 7

Substitute the value of $f(h(x))$ into the equation.
$g(f(h(x))) = (4\sqrt[4]{x} -6)^{3}$ So, $(g \circ f \circ h)(x) = (4\sqrt[4]{x} -6)^{3}$ .

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QuestionFind the function $(g \circ f \circ h)(x)$ for $f(x)=4x-6$ , $g(x)=x^3$ , and $h(x)=\sqrt[4]{x}$ .

Studdy Solution

STEP 1

Assumptions1. The function $f(x)=4x-6$ . The function $g(x)=x^{3}$
3. The function $h(x)=\sqrt[4]{x}$
4. We are asked to find the composition of functions $(g \circ f \circ h)(x)$

STEP 2

The composition of functions is a concept in mathematics where the output of one function becomes the input of another function. In other words, the output of the function $h(x)$ will be the input for the function $f(x)$ , and the output of $f(x)$ will be the input for $g(x)$ .

STEP 3

First, we need to find the output of $h(x)$ , which is $\sqrt[]{x}$ .

STEP 4

Next, we substitute the output of $h(x)$ into $f(x)$ , which is $4x-6$ . This gives us $f(h(x))$ .
$f(h(x)) =4h(x) -6$

STEP 5

Substitute the value of $h(x)$ into the equation.
$f(h(x)) =4\sqrt[4]{x} -$

STEP 6

Now, we substitute $f(h(x))$ into $g(x)$ , which is $x^{3}$ . This gives us $g(f(h(x)))$ .
$g(f(h(x))) = (f(h(x)))^{3}$

STEP 7

Substitute the value of $f(h(x))$ into the equation.
$g(f(h(x))) = (4\sqrt[4]{x} -6)^{3}$ So, $(g \circ f \circ h)(x) = (4\sqrt[4]{x} -6)^{3}$ .

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QuestionFind the function (g∘f∘h)(x)(g \circ f \circ h)(x)(g∘f∘h)(x) for f(x)=4x−6f(x)=4x-6f(x)=4x−6, g(x)=x3g(x)=x^3g(x)=x3, and h(x)=x4h(x)=\sqrt[4]{x}h(x)=4x​.

Studdy Solution

STEP 1

Assumptions1. The function f(x)=4x−6f(x)=4x-6f(x)=4x−6 . The function g(x)=x3g(x)=x^{3}g(x)=x33. The function h(x)=x4h(x)=\sqrt[4]{x}h(x)=4x​4. We are asked to find the composition of functions (g∘f∘h)(x)(g \circ f \circ h)(x)(g∘f∘h)(x)

STEP 2

STEP 3

First, we need to find the output of h(x)h(x)h(x), which is x\sqrt[]{x}x​.

STEP 4

Next, we substitute the output of h(x)h(x)h(x) into f(x)f(x)f(x), which is 4x−64x-64x−6. This gives us f(h(x))f(h(x))f(h(x)).f(h(x))=4h(x)−6f(h(x)) =4h(x) -6f(h(x))=4h(x)−6

STEP 5

Substitute the value of h(x)h(x)h(x) into the equation.f(h(x))=4x4−f(h(x)) =4\sqrt[4]{x} -f(h(x))=44x​−

STEP 6

Now, we substitute f(h(x))f(h(x))f(h(x)) into g(x)g(x)g(x), which is x3x^{3}x3. This gives us g(f(h(x)))g(f(h(x)))g(f(h(x))).g(f(h(x)))=(f(h(x)))3g(f(h(x))) = (f(h(x)))^{3}g(f(h(x)))=(f(h(x)))3

STEP 7

Substitute the value of f(h(x))f(h(x))f(h(x)) into the equation.g(f(h(x)))=(4x4−6)3g(f(h(x))) = (4\sqrt[4]{x} -6)^{3}g(f(h(x)))=(44x​−6)3So, (g∘f∘h)(x)=(4x4−6)3(g \circ f \circ h)(x) = (4\sqrt[4]{x} -6)^{3}(g∘f∘h)(x)=(44x​−6)3.

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QuestionFind the function $(g \circ f \circ h)(x)$ for $f(x)=4x-6$ , $g(x)=x^3$ , and $h(x)=\sqrt[4]{x}$ .

Assumptions1. The function $f(x)=4x-6$ . The function $g(x)=x^{3}$
3. The function $h(x)=\sqrt[4]{x}$
4. We are asked to find the composition of functions $(g \circ f \circ h)(x)$

First, we need to find the output of $h(x)$ , which is $\sqrt[]{x}$ .

Next, we substitute the output of $h(x)$ into $f(x)$ , which is $4x-6$ . This gives us $f(h(x))$ .
$f(h(x)) =4h(x) -6$

Substitute the value of $h(x)$ into the equation.
$f(h(x)) =4\sqrt[4]{x} -$

Now, we substitute $f(h(x))$ into $g(x)$ , which is $x^{3}$ . This gives us $g(f(h(x)))$ .
$g(f(h(x))) = (f(h(x)))^{3}$

Substitute the value of $f(h(x))$ into the equation.
$g(f(h(x))) = (4\sqrt[4]{x} -6)^{3}$ So, $(g \circ f \circ h)(x) = (4\sqrt[4]{x} -6)^{3}$ .