a function is called an odd function if f(-x)= -f(x).
a)show that f(x)=x^3-3x is an odd function.
b)by using the reult of (a),find the value of f(99)+f(-99)
f.4 maths
2007-10-16 6:17 am
回答 (5)
2007-10-16 6:23 am
✔ 最佳答案
a) f(-x) = (-x)^3 -3(-x)
= -x^3 + 3x
= -(x^3 - 3x)
= -f(x)
So f(x) is an odd function.
b) By (a), f(-99) = -f(99)
So f(99) + f(-99)
= f(99) - f(99)
= 0
2007-10-16 7:33 am
a) Firstly , f(-x) = -x^3 + 3x
-f(x) = -x^3+ 3x
= f(-x)
b) f(99) + f(-99) = f(99) - f(99) By (a)
= 0
-f(x) = -x^3+ 3x
= f(-x)
b) f(99) + f(-99) = f(99) - f(99) By (a)
= 0
2007-10-16 6:26 am
a)f(-x)=(-x)^3+3x
={(-1)^3}x^3+3x
= -x^3+3x
= -f(x)
b)f(99)+f(-99)=f(99)-f(99)
=0
={(-1)^3}x^3+3x
= -x^3+3x
= -f(x)
b)f(99)+f(-99)=f(99)-f(99)
=0
參考: myself
2007-10-16 6:24 am
a) Firstly , f(-x) = -x^3 + 3x
-f(x) = -x^3+ 3x
= f(-x)
b) f(99) + f(-99) = f(99) - f(99) By (a)
= 0
-f(x) = -x^3+ 3x
= f(-x)
b) f(99) + f(-99) = f(99) - f(99) By (a)
= 0
參考: me
2007-10-16 6:24 am
a. Let y = -x
-y = x
f(x) = x^3-3x
f(-y) = (-y)^3 - 3(-y)
= -y^3 + 3y
= - (y^3 - 3y)
= - f (y)
Therefore, f(-x) = -f(x)
b. f(99) + f(-99)
=f(99) + [ - f(99) ]
= 0
-y = x
f(x) = x^3-3x
f(-y) = (-y)^3 - 3(-y)
= -y^3 + 3y
= - (y^3 - 3y)
= - f (y)
Therefore, f(-x) = -f(x)
b. f(99) + f(-99)
=f(99) + [ - f(99) ]
= 0
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