Math / Algebra

QuestionUse the tables to evaluate the expressions. \begin{tabular}{|c|c|c|c|c|} \hline $x$ & 1 & 2 & 4 & 7 \\ \hline $f(x)$ & 4 & 7 & 1 & 2 \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|c|} \hline $x$ & 1 & 2 & 4 & 7 \\ \hline $g(x)$ & 2 & 4 & 7 & 8 \\ \hline \end{tabular}
Find $(g \circ f)(2)$ . Select the correct choice below and fill in any answer boxes within your choice. A. $(g \circ f)(2)=8$ B. The value is undefined.
Find $(\mathrm{f} \circ \mathrm{g})(4)$ . Select the correct choice below and fill in any answer boxes within your choice. A. $(\mathrm{f} \circ \mathrm{g})(4) \mathrm{F}$ $\square$ B. The value is undefined.

Studdy Solution

STEP 1

What is this asking? We need to find the function values when we combine the functions $f(x)$ and $g(x)$ in a specific order, using the given tables. Watch out! The order matters! $(f \circ g)(x)$ is not the same as $(g \circ f)(x)$ .
Also, make sure to use the correct table for each function!

STEP 2

1. Evaluate $(g \circ f)(2)$
2. Evaluate $(f \circ g)(4)$

STEP 3

$(g \circ f)(2)$ means $g(f(2))$ .
So, we first find $f(2)$ and then plug that result into $g(x)$ .

STEP 4

Looking at the table for $f(x)$ , when $x = \mathbf{2}$ , $f(x) = \mathbf{7}$ .
So, $f(2) = \mathbf{7}$ .

STEP 5

Since $f(2) = \mathbf{7}$ , we now need to find $g(\mathbf{7})$ .
Looking at the table for $g(x)$ , when $x = \mathbf{7}$ , $g(x) = \mathbf{8}$ .
Therefore, $(g \circ f)(2) = g(f(2)) = g(\mathbf{7}) = \mathbf{8}$ .

STEP 6

$(f \circ g)(4)$ means $f(g(4))$ .
So, we first find $g(4)$ and then plug that result into $f(x)$ .

STEP 7

Looking at the table for $g(x)$ , when $x = \mathbf{4}$ , $g(x) = \mathbf{7}$ .
So, $g(4) = \mathbf{7}$ .

STEP 8

Since $g(4) = \mathbf{7}$ , we now need to find $f(\mathbf{7})$ .
Looking at the table for $f(x)$ , when $x = \mathbf{7}$ , $f(x) = \mathbf{2}$ .
Therefore, $(f \circ g)(4) = f(g(4)) = f(\mathbf{7}) = \mathbf{2}$ .

STEP 9

$(g \circ f)(2) = \mathbf{8}$ .
This corresponds to choice A. $(f \circ g)(4) = \mathbf{2}$ .
This corresponds to choice A, with $\mathbf{2}$ filled in the box.

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Studdy Solution

STEP 1

What is this asking? We need to find the function values when we combine the functions $f(x)$ and $g(x)$ in a specific order, using the given tables. Watch out! The order matters! $(f \circ g)(x)$ is not the same as $(g \circ f)(x)$ .
Also, make sure to use the correct table for each function!

STEP 2

1. Evaluate $(g \circ f)(2)$
2. Evaluate $(f \circ g)(4)$

STEP 3

$(g \circ f)(2)$ means $g(f(2))$ .
So, we first find $f(2)$ and then plug that result into $g(x)$ .

STEP 4

Looking at the table for $f(x)$ , when $x = \mathbf{2}$ , $f(x) = \mathbf{7}$ .
So, $f(2) = \mathbf{7}$ .

STEP 5

Since $f(2) = \mathbf{7}$ , we now need to find $g(\mathbf{7})$ .
Looking at the table for $g(x)$ , when $x = \mathbf{7}$ , $g(x) = \mathbf{8}$ .
Therefore, $(g \circ f)(2) = g(f(2)) = g(\mathbf{7}) = \mathbf{8}$ .

STEP 6

$(f \circ g)(4)$ means $f(g(4))$ .
So, we first find $g(4)$ and then plug that result into $f(x)$ .

STEP 7

Looking at the table for $g(x)$ , when $x = \mathbf{4}$ , $g(x) = \mathbf{7}$ .
So, $g(4) = \mathbf{7}$ .

STEP 8

Since $g(4) = \mathbf{7}$ , we now need to find $f(\mathbf{7})$ .
Looking at the table for $f(x)$ , when $x = \mathbf{7}$ , $f(x) = \mathbf{2}$ .
Therefore, $(f \circ g)(4) = f(g(4)) = f(\mathbf{7}) = \mathbf{2}$ .

STEP 9

$(g \circ f)(2) = \mathbf{8}$ .
This corresponds to choice A. $(f \circ g)(4) = \mathbf{2}$ .
This corresponds to choice A, with $\mathbf{2}$ filled in the box.

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Studdy Solution

STEP 1

STEP 2

1. Evaluate (g∘f)(2)(g \circ f)(2)(g∘f)(2)2. Evaluate (f∘g)(4)(f \circ g)(4)(f∘g)(4)

STEP 3

(g∘f)(2)(g \circ f)(2)(g∘f)(2) means g(f(2))g(f(2))g(f(2)).So, we **first** find f(2)f(2)f(2) and **then** plug that result into g(x)g(x)g(x).

STEP 4

Looking at the table for f(x)f(x)f(x), when x=2x = \mathbf{2}x=2, f(x)=7f(x) = \mathbf{7}f(x)=7.So, f(2)=7f(2) = \mathbf{7}f(2)=7.

STEP 5

Since f(2)=7f(2) = \mathbf{7}f(2)=7, we now need to find g(7)g(\mathbf{7})g(7).Looking at the table for g(x)g(x)g(x), when x=7x = \mathbf{7}x=7, g(x)=8g(x) = \mathbf{8}g(x)=8.Therefore, (g∘f)(2)=g(f(2))=g(7)=8(g \circ f)(2) = g(f(2)) = g(\mathbf{7}) = \mathbf{8}(g∘f)(2)=g(f(2))=g(7)=8.

STEP 6

(f∘g)(4)(f \circ g)(4)(f∘g)(4) means f(g(4))f(g(4))f(g(4)).So, we **first** find g(4)g(4)g(4) and **then** plug that result into f(x)f(x)f(x).

STEP 7

Looking at the table for g(x)g(x)g(x), when x=4x = \mathbf{4}x=4, g(x)=7g(x) = \mathbf{7}g(x)=7.So, g(4)=7g(4) = \mathbf{7}g(4)=7.

STEP 8

Since g(4)=7g(4) = \mathbf{7}g(4)=7, we now need to find f(7)f(\mathbf{7})f(7).Looking at the table for f(x)f(x)f(x), when x=7x = \mathbf{7}x=7, f(x)=2f(x) = \mathbf{2}f(x)=2.Therefore, (f∘g)(4)=f(g(4))=f(7)=2(f \circ g)(4) = f(g(4)) = f(\mathbf{7}) = \mathbf{2}(f∘g)(4)=f(g(4))=f(7)=2.

STEP 9

(g∘f)(2)=8(g \circ f)(2) = \mathbf{8}(g∘f)(2)=8.This corresponds to choice A. (f∘g)(4)=2(f \circ g)(4) = \mathbf{2}(f∘g)(4)=2.This corresponds to choice A, with 2\mathbf{2}2 filled in the box.

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1. Evaluate $(g \circ f)(2)$
2. Evaluate $(f \circ g)(4)$

$(g \circ f)(2)$ means $g(f(2))$ .
So, we first find $f(2)$ and then plug that result into $g(x)$ .

Looking at the table for $f(x)$ , when $x = \mathbf{2}$ , $f(x) = \mathbf{7}$ .
So, $f(2) = \mathbf{7}$ .

Since $f(2) = \mathbf{7}$ , we now need to find $g(\mathbf{7})$ .
Looking at the table for $g(x)$ , when $x = \mathbf{7}$ , $g(x) = \mathbf{8}$ .
Therefore, $(g \circ f)(2) = g(f(2)) = g(\mathbf{7}) = \mathbf{8}$ .

$(f \circ g)(4)$ means $f(g(4))$ .
So, we first find $g(4)$ and then plug that result into $f(x)$ .

Looking at the table for $g(x)$ , when $x = \mathbf{4}$ , $g(x) = \mathbf{7}$ .
So, $g(4) = \mathbf{7}$ .

Since $g(4) = \mathbf{7}$ , we now need to find $f(\mathbf{7})$ .
Looking at the table for $f(x)$ , when $x = \mathbf{7}$ , $f(x) = \mathbf{2}$ .
Therefore, $(f \circ g)(4) = f(g(4)) = f(\mathbf{7}) = \mathbf{2}$ .

$(g \circ f)(2) = \mathbf{8}$ .
This corresponds to choice A. $(f \circ g)(4) = \mathbf{2}$ .
This corresponds to choice A, with $\mathbf{2}$ filled in the box.