Funkcja f jest okeślona wzorem f(x) = (1-x)(x+1) + 2x. Wyznacz zbiór wartości.
f(x) = (1-x)(x+1) + 2x
f(x) = (1-x)(1+x) + 2x
f(x) = 1 - x^2 + 2x
y = -x^2 + 2x +1
D = b^2 - 4ac = 2^2 - 4*(-1)*1 = 4+4
D = 8
a = -1 < 0
Yw = q = -D/4a (maksimum dla a < 0)
q = -8/4(-1) = -8/(-4) = 2
ZW =(-oo; 2>
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f(x) = (1-x)(x+1) + 2x
f(x) = (1-x)(1+x) + 2x
f(x) = 1 - x^2 + 2x
y = -x^2 + 2x +1
D = b^2 - 4ac = 2^2 - 4*(-1)*1 = 4+4
D = 8
a = -1 < 0
Yw = q = -D/4a (maksimum dla a < 0)
q = -8/4(-1) = -8/(-4) = 2
ZW =(-oo; 2>