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Sagot :
To find the inverse function [tex]\( N(a) \)[/tex] of the function [tex]\( A(n) = 3n - 20 \)[/tex], we need to express [tex]\( n \)[/tex] in terms of [tex]\( a \)[/tex].
Here are the steps we will take:
1. Start with the original function:
[tex]\[ A(n) = 3n - 20 \][/tex]
2. Replace [tex]\( A(n) \)[/tex] with [tex]\( a \)[/tex]: This is the first step in finding the inverse. By setting [tex]\( A(n) = a \)[/tex], we get:
[tex]\[ a = 3n - 20 \][/tex]
3. Solve for [tex]\( n \)[/tex]: We need to isolate [tex]\( n \)[/tex]. To do this, first add 20 to both sides of the equation:
[tex]\[ a + 20 = 3n \][/tex]
4. Divide both sides by 3: To completely isolate [tex]\( n \)[/tex], divide both sides of the equation by 3:
[tex]\[ n = \frac{a + 20}{3} \][/tex]
So the inverse function [tex]\( N(a) \)[/tex] is:
[tex]\[ N(a) = \frac{a + 20}{3} \][/tex]
Considering the provided options, the correct answer is:
C. [tex]\( N(a) = \frac{a + 20}{3} \)[/tex]
Here are the steps we will take:
1. Start with the original function:
[tex]\[ A(n) = 3n - 20 \][/tex]
2. Replace [tex]\( A(n) \)[/tex] with [tex]\( a \)[/tex]: This is the first step in finding the inverse. By setting [tex]\( A(n) = a \)[/tex], we get:
[tex]\[ a = 3n - 20 \][/tex]
3. Solve for [tex]\( n \)[/tex]: We need to isolate [tex]\( n \)[/tex]. To do this, first add 20 to both sides of the equation:
[tex]\[ a + 20 = 3n \][/tex]
4. Divide both sides by 3: To completely isolate [tex]\( n \)[/tex], divide both sides of the equation by 3:
[tex]\[ n = \frac{a + 20}{3} \][/tex]
So the inverse function [tex]\( N(a) \)[/tex] is:
[tex]\[ N(a) = \frac{a + 20}{3} \][/tex]
Considering the provided options, the correct answer is:
C. [tex]\( N(a) = \frac{a + 20}{3} \)[/tex]
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