QuestionFind the simplified fraction of the function $(m \circ n)(x)$ where $m(x)=\sqrt{x+9}$ and $n(x)=x+6$ .

Studdy Solution

STEP 1

Assumptions1. The function $m(x)=\sqrt{x+9}$ . The function $n(x)=x+6$
3. We need to find the function $(m \circ n)(x)$ , which represents the composition of functions $m$ and $n$

STEP 2

The composition of two functions, $m$ and $n$ , is defined as $(m \circ n)(x) = m(n(x))$ . This means that we substitute $n(x)$ into the function $m(x)$ .

STEP 3

Now, let's substitute $n(x)$ into $m(x)$ .
$(m \circ n)(x) = m(n(x)) = \sqrt{n(x)+9}$

STEP 4

Substitute $n(x)$ with its given function $x+6$ .
$(m \circ n)(x) = \sqrt{(x+6)+9}$

STEP 5

implify the expression under the square root.
$(m \circ n)(x) = \sqrt{x+15}$ So, the simplified fraction of the function $(m \circ n)(x)$ is $\sqrt{x+15}$ .

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QuestionFind the simplified fraction of the function $(m \circ n)(x)$ where $m(x)=\sqrt{x+9}$ and $n(x)=x+6$ .

Studdy Solution

STEP 1

Assumptions1. The function $m(x)=\sqrt{x+9}$ . The function $n(x)=x+6$
3. We need to find the function $(m \circ n)(x)$ , which represents the composition of functions $m$ and $n$

STEP 2

The composition of two functions, $m$ and $n$ , is defined as $(m \circ n)(x) = m(n(x))$ . This means that we substitute $n(x)$ into the function $m(x)$ .

STEP 3

Now, let's substitute $n(x)$ into $m(x)$ .
$(m \circ n)(x) = m(n(x)) = \sqrt{n(x)+9}$

STEP 4

Substitute $n(x)$ with its given function $x+6$ .
$(m \circ n)(x) = \sqrt{(x+6)+9}$

STEP 5

implify the expression under the square root.
$(m \circ n)(x) = \sqrt{x+15}$ So, the simplified fraction of the function $(m \circ n)(x)$ is $\sqrt{x+15}$ .

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QuestionFind the simplified fraction of the function (m∘n)(x)(m \circ n)(x)(m∘n)(x) where m(x)=x+9m(x)=\sqrt{x+9}m(x)=x+9​ and n(x)=x+6n(x)=x+6n(x)=x+6.

Studdy Solution

STEP 1

Assumptions1. The function m(x)=x+9m(x)=\sqrt{x+9}m(x)=x+9​ . The function n(x)=x+6n(x)=x+6n(x)=x+63. We need to find the function (m∘n)(x)(m \circ n)(x)(m∘n)(x), which represents the composition of functions mmm and nnn

STEP 2

The composition of two functions, mmm and nnn, is defined as (m∘n)(x)=m(n(x))(m \circ n)(x) = m(n(x))(m∘n)(x)=m(n(x)). This means that we substitute n(x)n(x)n(x) into the function m(x)m(x)m(x).

STEP 3

Now, let's substitute n(x)n(x)n(x) into m(x)m(x)m(x).(m∘n)(x)=m(n(x))=n(x)+9(m \circ n)(x) = m(n(x)) = \sqrt{n(x)+9}(m∘n)(x)=m(n(x))=n(x)+9​

STEP 4

Substitute n(x)n(x)n(x) with its given function x+6x+6x+6.(m∘n)(x)=(x+6)+9(m \circ n)(x) = \sqrt{(x+6)+9}(m∘n)(x)=(x+6)+9​

STEP 5

implify the expression under the square root.(m∘n)(x)=x+15(m \circ n)(x) = \sqrt{x+15}(m∘n)(x)=x+15​So, the simplified fraction of the function (m∘n)(x)(m \circ n)(x)(m∘n)(x) is x+15\sqrt{x+15}x+15​.

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QuestionFind the simplified fraction of the function $(m \circ n)(x)$ where $m(x)=\sqrt{x+9}$ and $n(x)=x+6$ .

Assumptions1. The function $m(x)=\sqrt{x+9}$ . The function $n(x)=x+6$
3. We need to find the function $(m \circ n)(x)$ , which represents the composition of functions $m$ and $n$

The composition of two functions, $m$ and $n$ , is defined as $(m \circ n)(x) = m(n(x))$ . This means that we substitute $n(x)$ into the function $m(x)$ .

Now, let's substitute $n(x)$ into $m(x)$ .
$(m \circ n)(x) = m(n(x)) = \sqrt{n(x)+9}$

Substitute $n(x)$ with its given function $x+6$ .
$(m \circ n)(x) = \sqrt{(x+6)+9}$

implify the expression under the square root.
$(m \circ n)(x) = \sqrt{x+15}$ So, the simplified fraction of the function $(m \circ n)(x)$ is $\sqrt{x+15}$ .