QuestionFind $(k \circ m)(x)$ and $(m \circ k)(x)$ for $k(x)=9x-5$ and $m(x)=x^2$ . Are they equal?

Studdy Solution

STEP 1

Assumptions1. We are given two functions $k(x)=9x-5$ and $m(x)=x^{}$ . . We need to find the composition of these functions, denoted as $(k \circ m)(x)$ .

STEP 2

The composition of functions is defined as the application of one function to the result of another. Mathematically, it can be represented as follows $(k \circ m)(x) = k(m(x))$

STEP 3

We know that $m(x) = x^{2}$ . So, we need to substitute $m(x)$ into the function $k(x)$ .
$k(m(x)) = k(x^{2})$

STEP 4

Now, substitute $x^{2}$ into $k(x)$ in place of $x$ .
$k(x^{2}) =9(x^{2}) -$

STEP 5

implify the expression to find the result of $(k \circ m)(x)$ .
$(k \circ m)(x) =9x^{2} -5$ So, $(k \circ m)(x) =9x^{2} -5$ .

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QuestionFind $(k \circ m)(x)$ and $(m \circ k)(x)$ for $k(x)=9x-5$ and $m(x)=x^2$ . Are they equal?

Studdy Solution

STEP 1

Assumptions1. We are given two functions $k(x)=9x-5$ and $m(x)=x^{}$ . . We need to find the composition of these functions, denoted as $(k \circ m)(x)$ .

STEP 2

The composition of functions is defined as the application of one function to the result of another. Mathematically, it can be represented as follows $(k \circ m)(x) = k(m(x))$

STEP 3

We know that $m(x) = x^{2}$ . So, we need to substitute $m(x)$ into the function $k(x)$ .
$k(m(x)) = k(x^{2})$

STEP 4

Now, substitute $x^{2}$ into $k(x)$ in place of $x$ .
$k(x^{2}) =9(x^{2}) -$

STEP 5

implify the expression to find the result of $(k \circ m)(x)$ .
$(k \circ m)(x) =9x^{2} -5$ So, $(k \circ m)(x) =9x^{2} -5$ .

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QuestionFind (k∘m)(x)(k \circ m)(x)(k∘m)(x) and (m∘k)(x)(m \circ k)(x)(m∘k)(x) for k(x)=9x−5k(x)=9x-5k(x)=9x−5 and m(x)=x2m(x)=x^2m(x)=x2. Are they equal?

Studdy Solution

STEP 1

Assumptions1. We are given two functions k(x)=9x−5k(x)=9x-5k(x)=9x−5 and m(x)=xm(x)=x^{}m(x)=x. . We need to find the composition of these functions, denoted as (k∘m)(x)(k \circ m)(x)(k∘m)(x).

STEP 2

The composition of functions is defined as the application of one function to the result of another. Mathematically, it can be represented as follows(k∘m)(x)=k(m(x))(k \circ m)(x) = k(m(x))(k∘m)(x)=k(m(x))

STEP 3

We know that m(x)=x2m(x) = x^{2}m(x)=x2. So, we need to substitute m(x)m(x)m(x) into the function k(x)k(x)k(x).k(m(x))=k(x2)k(m(x)) = k(x^{2})k(m(x))=k(x2)

STEP 4

Now, substitute x2x^{2}x2 into k(x)k(x)k(x) in place of xxx.k(x2)=9(x2)−k(x^{2}) =9(x^{2}) -k(x2)=9(x2)−

STEP 5

implify the expression to find the result of (k∘m)(x)(k \circ m)(x)(k∘m)(x).(k∘m)(x)=9x2−5(k \circ m)(x) =9x^{2} -5(k∘m)(x)=9x2−5So, (k∘m)(x)=9x2−5(k \circ m)(x) =9x^{2} -5(k∘m)(x)=9x2−5.

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QuestionFind $(k \circ m)(x)$ and $(m \circ k)(x)$ for $k(x)=9x-5$ and $m(x)=x^2$ . Are they equal?

Assumptions1. We are given two functions $k(x)=9x-5$ and $m(x)=x^{}$ . . We need to find the composition of these functions, denoted as $(k \circ m)(x)$ .

The composition of functions is defined as the application of one function to the result of another. Mathematically, it can be represented as follows $(k \circ m)(x) = k(m(x))$

We know that $m(x) = x^{2}$ . So, we need to substitute $m(x)$ into the function $k(x)$ .
$k(m(x)) = k(x^{2})$

Now, substitute $x^{2}$ into $k(x)$ in place of $x$ .
$k(x^{2}) =9(x^{2}) -$

implify the expression to find the result of $(k \circ m)(x)$ .
$(k \circ m)(x) =9x^{2} -5$ So, $(k \circ m)(x) =9x^{2} -5$ .