Question

求下列函数的反函数（麻烦写出过程）

(1)y=2sin3x (2) y=1+ln(x+2)

Answer 1

(1) y = 2sin3x, 值域 -2 ≤ y ≤ 2.
sin3x = y/2, 3x = arcsin(y/2), x = (1/3)arcsin(y/2),
反函数 y = (1/3)arcsin(x/2), 定义域 -2 ≤ x ≤ 2.
(2) y = 1+ln(x+2), 值域 -∞冲贺 < y < +∞.
ln(x+2) = y-1, x+2 = e^(y-1), x = e^(y-1) - 2,
反函数 y = e^(x-1) - 2, 定义老梁域 -∞ < x <侍判运 +∞.

Answer 2

(1)y=2sin3x
sin3x=y/2
3x=arsin(y/洞吵答2)
x=(1/碰碰3)arsin(y/2)
反函数 : y=(1/3)arsin(x/2)
(2)y=1+ln(x+2)
ln(x+2) =y-1
x+2=e^(y-1)
x=-2+e^(y-1)
反函数纳慧 : y=-2+e^(x-1)

Answer 3

(1)

y=2sin3x
sin3x=y/让帆2
3x=arsin(y/2)
x=(1/3)arsin(y/悔誉2)
反坦前雹函数 : y=(1/3)arsin(x/2)
(2)
y=1+ln(x+2)
ln(x+2) =y-1
x+2=e^(y-1)
x=-2+e^(y-1)
反函数 : y=-2+e^(x-1)

Answer 4

交换xy的局纤位缓销置扰腊游
(1)x=2sin3y
3y=arcsin(x/2)
y=(1/3)arsin(x/2)
(2)x=1+ln(y+2)
x-1=ln(y+2)
e^(x-1)=y+2
y=e^(x-1)-2