SOLUTION: if h(x+1)=3h(x)+4 over 3 for all positive integers x and h(1)= -2/3, what is the value of h(3)

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Question 1043435: if h(x+1)=3h(x)+4 over 3 for all positive integers x and h(1)= -2/3, what is the value of h(3)
Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
if h(x+1)=3h(x)+4 over 3 for all positive integers x and h(1)= -2/3,
what is the value of h(3)
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Question:: What is it that is "over 3"?
Please use parenthesis to indicate numerator and denominator
Cheers,
Stan H.
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Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
What's "over 3" mean, the whole 3h(x)+4 over 3 or just the 4
over 3?

Assuming you meant %22h%28x%2B1%29%22%29%22%22=%22%22%283%2A%22h%28x%29%22%2B4%29%2F3

Let x=1 in 

%22h%28x%2B1%29%22%29%22%22=%22%22%283%2A%22h%28x%29%22%2B4%29%2F3
%22h%281%2B1%29%22%29%22%22=%22%22%283%2A%22h%281%29%22%2B4%29%2F3
%22h%282%29%22%29%22%22=%22%22%283%2A%22h%281%29%22%2B4%29%2F3
%22h%282%29%22%29%22%22=%22%22%283%2A%28-2%2F3%29%2B4%29%2F3
%22h%282%29%22%29%22%22=%22%22%28-2%2B4%29%2F3
%22h%282%29%22%29%22%22=%22%222%2F3

Let x=2 in 

%22h%28x%2B1%29%22%29%22%22=%22%22%283%2A%22h%28x%29%22%2B4%29%2F3
%22h%282%2B1%29%22%29%22%22=%22%22%283%2A%22h%282%29%22%2B4%29%2F3
%22h%283%29%22%29%22%22=%22%22%283%2A%222%2F3%22%2B4%29%2F3
%22h%283%29%22%29%22%22=%22%22%282%2B4%29%2F3
%22h%283%29%22%29%22%22=%22%22%286%29%2F3
%22h%283%29%22%29%22%22=%22%222

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Assuming you meant %22h%28x%2B1%29%22%29%22%22=%22%223%2A%22h%28x%29%22%2B4%2F3

Let x=1 in 

%22h%28x%2B1%29%22%29%22%22=%22%223%2A%22h%28x%29%22%2B4%2F3
%22h%281%2B1%29%22%29%22%22=%22%223%2A%22h%281%29%22%2B4%2F3
%22h%282%29%22%29%22%22=%22%223%2A%22h%281%29%22%2B4%2F3
%22h%282%29%22%29%22%22=%22%223%2A%28-2%2F3%29%2B4%2F3
%22h%282%29%22%29%22%22=%22%22-2%2B4%2F3
%22h%282%29%22%29%22%22=%22%22-6%2F3%2B4%2F3
%22h%282%29%22%29%22%22=%22%22-2%2F3

Let x=2 in 

%22h%28x%2B1%29%22%29%22%22=%22%223%2A%22h%28x%29%22%2B4%2F3
%22h%282%2B1%29%22%29%22%22=%22%223%2A%22h%282%29%22%2B4%29%2F3
%22h%283%29%22%29%22%22=%22%223%2A%28-2%2F3%29%2B4%2F3
%22h%283%29%22%29%22%22=%22%22-2%2B4%2F3
%22h%283%29%22%29%22%22=%22%22-6%2F3%2B4%2F3
%22h%283%29%22%29%22%22=%22%22-2%2F3

This is the more interesting case, since 
h%28x%29=+-2%2F3 for all values of x.  h(x)
is a constant function.

Edwin