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Funzione esponenziale

f(x) = 2^(x + m) + 2^(-x + 2·m + 1)

f(-x) = 2^(-x + m) + 2^(-(-x) + 2·m + 1)

f(-x)= 2^(x + 2·m + 1) + 2^(m - x)

pari: f(x) = f(-x)

2^(x + m) + 2^(-x + 2·m + 1) = 2^(x + 2·m + 1) + 2^(m - x)

2^(m - x)·(2^(2·x) + 2^(m + 1)) = 2^(m - x)·(2^(2·x + m + 1) + 1)

2^(2·x) + 2^(m + 1) = 2^(2·x + m + 1) + 1

2^(2·x) = t > 0

t + 2^(m + 1) = 2^(m + 1)·t + 1

2^(m + 1) = 1

m + 1 = 0---> m = -1

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f(x) = 2^(x + (-1)) + 2^(-x + 2·(-1) + 1)

f(x)= 2^(x - 1) + 2^(-x - 1)

2^(x - 1) + 2^(-x - 1) > 1

2^x = t > 0

t/2 + 1/(2·t) > 1

t/2 + 1/(2·t) - 1 > 0

(t - 1)^2/(2·t) > 0

(t - 1)^2 > 0---> t ≠ 1

2^x ≠ 2^0----> x ≠ 0