Y = f (x) is an odd function defined on R. when x > 0, f (x) = x & # 178; - 2x + 3, find the analytic expression of F (x) on R | Math enthusiast | Mathematical art

Y = f (x) is an odd function defined on R. when x > 0, f (x) = x & # 178; - 2x + 3, find the analytic expression of F (x) on R

Let x0, so we can substitute - x into the known function, f (- x) = (- x) ^ 2-2 (- x) + 3 = x ^ 2 + 2x + 3,
Because it is an odd function, the left f (- x) = - f (x),
F (x) = - x ^ 2-2x-3 (note that this formula only applies to x0)
0,x=0
-x^2-2x-3,x

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