SOLUTION: given f(x)=f(x+1)+3 and f(2)=5, what is the value of f(8)

Question 944944: given f(x)=f(x+1)+3 and f(2)=5, what is the value of f(8)
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
given f(x)=f(x+1)+3 and f(2)=5, what is the value of f(8)
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First isolate f(x+1)

f(x)=f(x+1)+3
f(x)-3=f(x+1)
f(x+1) = f(x) - 3
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Because f(x+1) = f(x) - 3, we need to build our way up to f(8) by finding f(7), f(6), etc all the way down until f(3)
So let's find f(3)

f(x+1) = f(x) - 3
f(2+1) = f(2) - 3
f(3) = f(2) - 3
f(3) = 5 - 3
f(3) = 2
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and then use this to find f(4)

f(x+1) = f(x) - 3
f(3+1) = f(3) - 3
f(4) = f(3) - 3
f(4) = 2 - 3
f(4) = -1
-------------------
we do the same for f(5)

f(x+1) = f(x) - 3
f(4+1) = f(4) - 3
f(5) = f(4) - 3
f(5) = -1 - 3
f(5) = -4
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and so on...until we reach f(8)

f(x+1) = f(x) - 3
f(5+1) = f(5) - 3
f(6) = f(5) - 3
f(6) = -4 - 3
f(6) = -7
-------------------
f(x+1) = f(x) - 3
f(6+1) = f(6) - 3
f(7) = f(6) - 3
f(7) = -7 - 3
f(7) = -10
-------------------
f(x+1) = f(x) - 3
f(7+1) = f(7) - 3
f(8) = f(7) - 3
f(8) = -10 - 3
f(8) = -13
-------------------

So in the end, we find that f(8) = -13
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