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agasfer [191]
3 years ago
7

If

"latex-formula">, prove that f(x) + f(x+1)=4f(x)
Mathematics
1 answer:
SOVA2 [1]3 years ago
8 0

$f(x)+f(x+1) \stackrel{1}{=} 3^x+3^{x+1} \stackrel{2}{=} 3^x+3^x\cdot3^1\stackrel{3}{=}3^x+3\cdot3^x\stackrel{4}{=}4\cdot3^x\stackrel{5}{=}4\cdot f(x)

1) Substitution from definition.

2) We use $x^{a+b}=x^a\cdot x^b

3) We are changing the order of 3 and 3^x.

4) We add 1 and 3 3^x and we get 4\cdot 3^x

5) Substitution from definition (but the other way than at the beginning).

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<img src="https://tex.z-dn.net/?f=%3Cbr%3E%0Ay%3D%20x%5E%7B2%7D%20-9" id="TexFormula1" title="&amp;#10;y= x^{2} -9" alt="&amp;#1
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