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Sagot :
To determine the value of [tex]\( x \)[/tex] for which [tex]\((f-g)(x) = 0\)[/tex], we start by defining [tex]\((f-g)(x)\)[/tex]:
[tex]\[ (f-g)(x) = f(x) - g(x) \][/tex]
Given the functions [tex]\( f(x) = 16x - 30 \)[/tex] and [tex]\( g(x) = 14x - 6 \)[/tex], we can substitute these into the equation for [tex]\((f-g)(x)\)[/tex]:
[tex]\[ (f-g)(x) = (16x - 30) - (14x - 6) \][/tex]
Now, let's simplify the expression:
[tex]\[ (f-g)(x) = 16x - 30 - 14x + 6 \][/tex]
Combine like terms:
[tex]\[ (f-g)(x) = (16x - 14x) + (-30 + 6) \][/tex]
This simplifies to:
[tex]\[ (f-g)(x) = 2x - 24 \][/tex]
We want to find the value of [tex]\( x \)[/tex] for which [tex]\((f-g)(x) = 0\)[/tex]:
[tex]\[ 2x - 24 = 0 \][/tex]
To solve for [tex]\( x \)[/tex], first add 24 to both sides of the equation:
[tex]\[ 2x - 24 + 24 = 0 + 24 \][/tex]
This simplifies to:
[tex]\[ 2x = 24 \][/tex]
Next, divide both sides by 2 to isolate [tex]\( x \)[/tex]:
[tex]\[ x = \frac{24}{2} \][/tex]
So, we have:
[tex]\[ x = 12 \][/tex]
Thus, the value of [tex]\( x \)[/tex] that satisfies [tex]\((f-g)(x) = 0\)[/tex] is 12. Therefore, out of the given options, the correct answer is:
12
[tex]\[ (f-g)(x) = f(x) - g(x) \][/tex]
Given the functions [tex]\( f(x) = 16x - 30 \)[/tex] and [tex]\( g(x) = 14x - 6 \)[/tex], we can substitute these into the equation for [tex]\((f-g)(x)\)[/tex]:
[tex]\[ (f-g)(x) = (16x - 30) - (14x - 6) \][/tex]
Now, let's simplify the expression:
[tex]\[ (f-g)(x) = 16x - 30 - 14x + 6 \][/tex]
Combine like terms:
[tex]\[ (f-g)(x) = (16x - 14x) + (-30 + 6) \][/tex]
This simplifies to:
[tex]\[ (f-g)(x) = 2x - 24 \][/tex]
We want to find the value of [tex]\( x \)[/tex] for which [tex]\((f-g)(x) = 0\)[/tex]:
[tex]\[ 2x - 24 = 0 \][/tex]
To solve for [tex]\( x \)[/tex], first add 24 to both sides of the equation:
[tex]\[ 2x - 24 + 24 = 0 + 24 \][/tex]
This simplifies to:
[tex]\[ 2x = 24 \][/tex]
Next, divide both sides by 2 to isolate [tex]\( x \)[/tex]:
[tex]\[ x = \frac{24}{2} \][/tex]
So, we have:
[tex]\[ x = 12 \][/tex]
Thus, the value of [tex]\( x \)[/tex] that satisfies [tex]\((f-g)(x) = 0\)[/tex] is 12. Therefore, out of the given options, the correct answer is:
12
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