Question Find the values of $(f \circ g)(-5)$ , $(g \circ f)(15)$ , $(f \circ f)(6)$ , and $(g \circ g)(-3)$ using the given table of $f(x)$ and $g(x)$ .

Studdy Solution

STEP 1

Assumptions1. The table provides the values of two functions, $f(x)$ and $g(x)$ , at various points $x$ . . The function composition $(f \circ g)(x)$ means $f(g(x))$ .
3. The function composition $(g \circ f)(x)$ means $g(f(x))$ .

STEP 2

To find $(f \circ g)(-5)$ , we first look up the value of $g(-5)$ from the table.
$g(-5) =15$

STEP 3

Then, we substitute $g(-5)$ into $f(x)$ , so we look up the value of $f(15)$ from the table.
$f(15) =1$ So, $(f \circ g)(-5) =1$ .

STEP 4

To find $(g \circ f)(15)$ , we first look up the value of $f(15)$ from the table.
$f(15) =1$

STEP 5

Then, we substitute $f(15)$ into $g(x)$ , so we look up the value of $g(1)$ from the table.
$g(1) = -3$ So, $(g \circ f)(15) = -3$ .

STEP 6

To find $(f \circ f)(6)$ , we first look up the value of $f(6)$ from the table.
$f(6) =15$

STEP 7

Then, we substitute $f(6)$ into $f(x)$ again, so we look up the value of $f(15)$ from the table.
$f(15) =1$ So, $(f \circ f)(6) =1$ .

STEP 8

To find $(g \circ g)(-3)$ , we first look up the value of $g(-3)$ from the table.
$g(-3) =10$

STEP 9

Then, we substitute $g(-3)$ into $g(x)$ again, so we look up the value of $g()$ from the table.
$g() = -5$ So, $(g \circ g)(-3) = -5$ .
The solutions are $(f \circ g)(-5) =$
$(g \circ f)(15) = -3$
$(f \circ f)(6) =$
$(g \circ g)(-3) = -5$

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Question Find the values of $(f \circ g)(-5)$ , $(g \circ f)(15)$ , $(f \circ f)(6)$ , and $(g \circ g)(-3)$ using the given table of $f(x)$ and $g(x)$ .

Studdy Solution

STEP 1

Assumptions1. The table provides the values of two functions, $f(x)$ and $g(x)$ , at various points $x$ . . The function composition $(f \circ g)(x)$ means $f(g(x))$ .
3. The function composition $(g \circ f)(x)$ means $g(f(x))$ .

STEP 2

To find $(f \circ g)(-5)$ , we first look up the value of $g(-5)$ from the table.
$g(-5) =15$

STEP 3

Then, we substitute $g(-5)$ into $f(x)$ , so we look up the value of $f(15)$ from the table.
$f(15) =1$ So, $(f \circ g)(-5) =1$ .

STEP 4

To find $(g \circ f)(15)$ , we first look up the value of $f(15)$ from the table.
$f(15) =1$

STEP 5

Then, we substitute $f(15)$ into $g(x)$ , so we look up the value of $g(1)$ from the table.
$g(1) = -3$ So, $(g \circ f)(15) = -3$ .

STEP 6

To find $(f \circ f)(6)$ , we first look up the value of $f(6)$ from the table.
$f(6) =15$

STEP 7

Then, we substitute $f(6)$ into $f(x)$ again, so we look up the value of $f(15)$ from the table.
$f(15) =1$ So, $(f \circ f)(6) =1$ .

STEP 8

To find $(g \circ g)(-3)$ , we first look up the value of $g(-3)$ from the table.
$g(-3) =10$

STEP 9

Then, we substitute $g(-3)$ into $g(x)$ again, so we look up the value of $g()$ from the table.
$g() = -5$ So, $(g \circ g)(-3) = -5$ .
The solutions are $(f \circ g)(-5) =$
$(g \circ f)(15) = -3$
$(f \circ f)(6) =$
$(g \circ g)(-3) = -5$

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Question Find the values of (f∘g)(−5)(f \circ g)(-5)(f∘g)(−5), (g∘f)(15)(g \circ f)(15)(g∘f)(15), (f∘f)(6)(f \circ f)(6)(f∘f)(6), and (g∘g)(−3)(g \circ g)(-3)(g∘g)(−3) using the given table of f(x)f(x)f(x) and g(x)g(x)g(x).

Studdy Solution

STEP 1

Assumptions1. The table provides the values of two functions, f(x)f(x)f(x) and g(x)g(x)g(x), at various points xxx. . The function composition (f∘g)(x)(f \circ g)(x)(f∘g)(x) means f(g(x))f(g(x))f(g(x)).3. The function composition (g∘f)(x)(g \circ f)(x)(g∘f)(x) means g(f(x))g(f(x))g(f(x)).

STEP 2

To find (f∘g)(−5)(f \circ g)(-5)(f∘g)(−5), we first look up the value of g(−5)g(-5)g(−5) from the table.g(−5)=15g(-5) =15g(−5)=15

STEP 3

Then, we substitute g(−5)g(-5)g(−5) into f(x)f(x)f(x), so we look up the value of f(15)f(15)f(15) from the table.f(15)=1f(15) =1f(15)=1So, (f∘g)(−5)=1(f \circ g)(-5) =1(f∘g)(−5)=1.

STEP 4

To find (g∘f)(15)(g \circ f)(15)(g∘f)(15), we first look up the value of f(15)f(15)f(15) from the table.f(15)=1f(15) =1f(15)=1

STEP 5

Then, we substitute f(15)f(15)f(15) into g(x)g(x)g(x), so we look up the value of g(1)g(1)g(1) from the table.g(1)=−3g(1) = -3g(1)=−3So, (g∘f)(15)=−3(g \circ f)(15) = -3(g∘f)(15)=−3.

STEP 6

To find (f∘f)(6)(f \circ f)(6)(f∘f)(6), we first look up the value of f(6)f(6)f(6) from the table.f(6)=15f(6) =15f(6)=15

STEP 7

Then, we substitute f(6)f(6)f(6) into f(x)f(x)f(x) again, so we look up the value of f(15)f(15)f(15) from the table.f(15)=1f(15) =1f(15)=1So, (f∘f)(6)=1(f \circ f)(6) =1(f∘f)(6)=1.

STEP 8

To find (g∘g)(−3)(g \circ g)(-3)(g∘g)(−3), we first look up the value of g(−3)g(-3)g(−3) from the table.g(−3)=10g(-3) =10g(−3)=10

STEP 9

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Question Find the values of $(f \circ g)(-5)$ , $(g \circ f)(15)$ , $(f \circ f)(6)$ , and $(g \circ g)(-3)$ using the given table of $f(x)$ and $g(x)$ .

Assumptions1. The table provides the values of two functions, $f(x)$ and $g(x)$ , at various points $x$ . . The function composition $(f \circ g)(x)$ means $f(g(x))$ .
3. The function composition $(g \circ f)(x)$ means $g(f(x))$ .

To find $(f \circ g)(-5)$ , we first look up the value of $g(-5)$ from the table.
$g(-5) =15$

Then, we substitute $g(-5)$ into $f(x)$ , so we look up the value of $f(15)$ from the table.
$f(15) =1$ So, $(f \circ g)(-5) =1$ .

To find $(g \circ f)(15)$ , we first look up the value of $f(15)$ from the table.
$f(15) =1$

Then, we substitute $f(15)$ into $g(x)$ , so we look up the value of $g(1)$ from the table.
$g(1) = -3$ So, $(g \circ f)(15) = -3$ .

To find $(f \circ f)(6)$ , we first look up the value of $f(6)$ from the table.
$f(6) =15$

Then, we substitute $f(6)$ into $f(x)$ again, so we look up the value of $f(15)$ from the table.
$f(15) =1$ So, $(f \circ f)(6) =1$ .

To find $(g \circ g)(-3)$ , we first look up the value of $g(-3)$ from the table.
$g(-3) =10$