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Sagot :
To determine [tex]\((f - g)(-3)\)[/tex], we need to follow a detailed, step-by-step process.
First, let's define the functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]:
[tex]\[ f(x) = 3x^2 + 6 \][/tex]
[tex]\[ g(x) = -5x + 2 \][/tex]
We need to find the value of [tex]\((f - g)(-3)\)[/tex]. This means we will evaluate both [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] at [tex]\(x = -3\)[/tex], and then find the difference between these values.
1. Evaluate [tex]\(f(-3)\)[/tex]:
Substitute [tex]\(x = -3\)[/tex] into the function [tex]\(f(x)\)[/tex]:
[tex]\[ f(-3) = 3(-3)^2 + 6 \][/tex]
Calculate [tex]\((-3)^2\)[/tex]:
[tex]\[ (-3)^2 = 9 \][/tex]
Now, multiply by 3:
[tex]\[ 3 \cdot 9 = 27 \][/tex]
Add 6:
[tex]\[ 27 + 6 = 33 \][/tex]
Therefore:
[tex]\[ f(-3) = 33 \][/tex]
2. Evaluate [tex]\(g(-3)\)[/tex]:
Substitute [tex]\(x = -3\)[/tex] into the function [tex]\(g(x)\)[/tex]:
[tex]\[ g(-3) = -5(-3) + 2 \][/tex]
Calculate [tex]\(-5 \cdot -3\)[/tex]:
[tex]\[ -5 \cdot -3 = 15 \][/tex]
Add 2:
[tex]\[ 15 + 2 = 17 \][/tex]
Therefore:
[tex]\[ g(-3) = 17 \][/tex]
3. Calculate [tex]\((f - g)(-3)\)[/tex]:
Subtract [tex]\(g(-3)\)[/tex] from [tex]\(f(-3)\)[/tex]:
[tex]\[ (f - g)(-3) = f(-3) - g(-3) \][/tex]
Substitute the values we found:
[tex]\[ (f - g)(-3) = 33 - 17 \][/tex]
Perform the subtraction:
[tex]\[ 33 - 17 = 16 \][/tex]
Thus:
[tex]\[ (f - g)(-3) = 16 \][/tex]
First, let's define the functions [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex]:
[tex]\[ f(x) = 3x^2 + 6 \][/tex]
[tex]\[ g(x) = -5x + 2 \][/tex]
We need to find the value of [tex]\((f - g)(-3)\)[/tex]. This means we will evaluate both [tex]\(f(x)\)[/tex] and [tex]\(g(x)\)[/tex] at [tex]\(x = -3\)[/tex], and then find the difference between these values.
1. Evaluate [tex]\(f(-3)\)[/tex]:
Substitute [tex]\(x = -3\)[/tex] into the function [tex]\(f(x)\)[/tex]:
[tex]\[ f(-3) = 3(-3)^2 + 6 \][/tex]
Calculate [tex]\((-3)^2\)[/tex]:
[tex]\[ (-3)^2 = 9 \][/tex]
Now, multiply by 3:
[tex]\[ 3 \cdot 9 = 27 \][/tex]
Add 6:
[tex]\[ 27 + 6 = 33 \][/tex]
Therefore:
[tex]\[ f(-3) = 33 \][/tex]
2. Evaluate [tex]\(g(-3)\)[/tex]:
Substitute [tex]\(x = -3\)[/tex] into the function [tex]\(g(x)\)[/tex]:
[tex]\[ g(-3) = -5(-3) + 2 \][/tex]
Calculate [tex]\(-5 \cdot -3\)[/tex]:
[tex]\[ -5 \cdot -3 = 15 \][/tex]
Add 2:
[tex]\[ 15 + 2 = 17 \][/tex]
Therefore:
[tex]\[ g(-3) = 17 \][/tex]
3. Calculate [tex]\((f - g)(-3)\)[/tex]:
Subtract [tex]\(g(-3)\)[/tex] from [tex]\(f(-3)\)[/tex]:
[tex]\[ (f - g)(-3) = f(-3) - g(-3) \][/tex]
Substitute the values we found:
[tex]\[ (f - g)(-3) = 33 - 17 \][/tex]
Perform the subtraction:
[tex]\[ 33 - 17 = 16 \][/tex]
Thus:
[tex]\[ (f - g)(-3) = 16 \][/tex]
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