SOLUTION: Given f(x)=2^x ... show that f(x+3)-f(x-1) = 15/2 f(x)

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Question 1041901: Given f(x)=2^x ... show that f(x+3)-f(x-1) = 15/2 f(x)
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
system%28f%28x%2B3%29=2%5E%28x%2B3%29%2Cf%28x-1%29=2%5E%28x-1%29%29

2%5E%28x%2B3%29-2%5E%28x-1%29

Rules for Exponents gives
%282%5Ex%29%282%5E3%29-%282%5Ex%29%282%5E%28-1%29%29

Distributive Property, in reverse gives
%282%5Ex%29%282%5E3-2%5E%28-1%29%29

%282%5Ex%29%282%5E3-1%2F2%29

%282%5Ex%29%288-1%2F2%29

%282%5Ex%29%2816%2F2-1%2F2%29

%282%5Ex%29%2815%2F2%29

%2815%2F2%29%282%5Ex%29

Substitute the given function def.
%2815%2F2%29f%28x%29-------Result to be proved, DONE.