Question

英文数学题.速度高分求解.

1.given the function f(x) = 2x*2 +5x -7, find the values of:
a) f(-2) b) f(4) c) f(x*2) d) (f(x))*2 e) f(x*2) -xf(x)
2.let f(x) =1/2 (2*x (符号是二的x次方) +2*-x (二的-x次方))
show that for any real values of x and y, f(x+y) +f (x-y) = 2f(x)f(y)
3. a) if f(x+1) =x*2 -3x +2, find f(x)
b) if f (1/x) = x+ 根号1+x*2, find f(x).

感激不尽!!!!!!
还有
a solid wodden sphere of radius 6cm is to be cut into a cube of side a cm. find the largest possible value of a.

Answer 1

1.given the function f(x) = 2x*2 +5x -7, find the values of:
a) f(-2) =8-10-7=-5
b) f(4)=32+20-7=45
c) f(x*2)=2x^4+5x^2-7
d) (f(x))*2=(2x^2+5x-7)^2=4x^4+10x^3-14x^2+10x^3+25x^2-35x-14x^2-35x+49
=4x^4+20x^3-28x^2-70x+49
e) f(x*2) -xf(x)=2x^4+5x^2-7-x(2x*2 +5x -7)=2x^4-2x^3+7x-7
2.let f(x) =1/2 (2*x (符号是二的x次方) +2*-x (二的-x次方))
show that for any real values of x and y, f(x+y) +f (x-y) = 2f(x)f(y)
f(x)=2^(x-1)+2^(-x-1)
f(x+y)+f(x-y)=2f(x)(y)
2^(x+y-1)+2^(-x-y-1)+2^(x-y-1)+2^(-x+y-1)=2[2^(x-1)+2^(-x-1)][2^(y-1)+2^(-y-1)]
2^(x+y-1)+2^(-x-y-1)+2^(x-y-1)+2^(-x+y-1)=[2^x+2^(-x)][2^(y-1)+2^(-y-1)]
2^(x+y-1)+2^(-x-y-1)+2^(x-y-1)+2^(-x+y-1)=2^(x+y-1)+2^(x-y-1)+2^(-x+y-1)+2^(-x-y-1)
等式恒成立，与xy无关，题目要求给出任一对值
可以有x=2,y=3
3. a) if f(x+1) =x*2 -3x +2, find f(x)
f(x+1) =x*2 -3x +2=(x+1)^2-5x-5+6
f(x)=x^2-5x+6
b) if f (1/x) = x+ 根号1+x*2, find f(x).
f (1/x) = x+ 根号1+x*2=1/(1/x)+根号(1+1/(1/x)^2)
f(x)=1/x+根号(1+1/x^2) (可以通分成以x为分母)

a solid wodden sphere of radius 6cm is to be cut into a cube of side a cm. find the largest possible value of a.
一个半径为6cm的球体要切成棱为acm的一个立方体。找到a最大值。
题目相当于在圆中找到最大的正方形
这时棱长最大为a=6根号2

Answer 2

1
a) f(-2) =8-10-7=-5
b) f(4)=32+20-7=45
c) f(x*2)=2x^4+5x^2-7
d) (f(x))*2=(2x^2+5x-7)^2=4x^4+10x^3-14x^2+10x^3+25x^2-35x-14x^2-35x+49
=4x^4+20x^3-28x^2-70x+49
e) f(x*2) -xf(x)=2x^4+5x^2-7-x(2x*2 +5x -7)=2x^4-2x^3+7x-7

2
f(x)=2^(x-1)+2^(-x-1)
f(x+y)+f(x-y)=2f(x)(y)
2^(x+y-1)+2^(-x-y-1)+2^(x-y-1)+2^(-x+y-1)=2[2^(x-1)+2^(-x-1)][2^(y-1)+2^(-y-1)]
2^(x+y-1)+2^(-x-y-1)+2^(x-y-1)+2^(-x+y-1)=[2^x+2^(-x)][2^(y-1)+2^(-y-1)]
2^(x+y-1)+2^(-x-y-1)+2^(x-y-1)+2^(-x+y-1)=2^(x+y-1)+2^(x-y-1)+2^(-x+y-1)+2^(-x-y-1)
等式恒成立，与xy无关，给出任一对值 x=2,y=3
3.
a) if f(x+1) =x*2 -3x +2, find f(x)
f(x+1) =x*2 -3x +2=(x+1)^2-5x-5+6
f(x)=x^2-5x+6
b) if f (1/x) = x+ 根号1+x*2, find f(x).
f (1/x) = x+ 根号1+x*2=1/(1/x)+根号(1+1/(1/x)^2)
f(x)=1/x+根号(1+1/x^2)

Answer 3

given the function f(x) = 2x*2 +5x -7, find the values of:
a) f(-2) =8-10-7=-5
b) f(4)=32+20-7=45
c) f(x*2)=2x^4+5x^2-7
d) (f(x))*2=(2x^2+5x-7)^2=4x^4+10x^3-14x^2+10x^3+25x^2-35x-14x^2-35x+49
=4x^4+20x^3-28x^2-70x+49
e) f(x*2) -xf(x)=2x^4+5x^2-7-x(2x*2 +5x -7)=2x^4-2x^3+7x-7
2.let f(x) =1/2 (2*x (符号是二的x次方) +2*-x (二的-x次方))
show that for any real values of x and y, f(x+y) +f (x-y) = 2f(x)f(y)
f(x)=2^(x-1)+2^(-x-1)
f(x+y)+f(x-y)=2f(x)(y)
2^(x+y-1)+2^(-x-y-1)+2^(x-y-1)+2^(-x+y-1)=2[2^(x-1)+2^(-x-1)][2^(y-1)+2^(-y-1)]
2^(x+y-1)+2^(-x-y-1)+2^(x-y-1)+2^(-x+y-1)=[2^x+2^(-x)][2^(y-1)+2^(-y-1)]
2^(x+y-1)+2^(-x-y-1)+2^(x-y-1)+2^(-x+y-1)=2^(x+y-1)+2^(x-y-1)+2^(-x+y-1)+2^(-x-y-1)
等式恒成立，与xy无关，题目要求给出任一对值
可以有x=2,y=3
3. a) if f(x+1) =x*2 -3x +2, find f(x)
f(x+1) =x*2 -3x +2=(x+1)^2-5x-5+6
f(x)=x^2-5x+6
b) if f (1/x) = x+ 根号1+x*2, find f(x).
f (1/x) = x+ 根号1+x*2=1/(1/x)+根号(1+1/(1/x)^2)
f(x)=1/x+根号(1+1/x^2) (可以通分成以x为分母)

Answer 4

最后一题应该是4√3cm

Answer 5

我的答案更好

Answer 6

1、2x-xy 2、x+y 3、a)5x+y b)2/x 问题补充：56cm