Question

求反函数两道题

y=x+2/x-2 y=1+lg(2x-3)

Answer 1

y=x+2/x-2
xy -2y = x+2
xy- x= 2+2y
x(y-1) = 2+2y
x= (2+2y)/(y-1)
所以： y = 2(x+1)/(x-1)

y=1+lg(2x-3)
y-1 = lg (2x-3)
10^(y-1) = 2x -3
2x= 3+ 10^(y-1)
x= 3/2 + 1/2 × 10^(y-1)
所以：y = 3/2 + 1/2× 10^(x-1)

有什么不明白可继续追问
请及时选为满意答案，谢谢

追问

这个题 lim(x趋于π/2）（1+cosx）^secx 3Q，希望能详细些

Answer 2

yx-2y=x+2
yx-x=2y+2
x=(2y+2)/(x-1)
所以反函数y=2(x+1)/(x-1)

lg(2x-3)=y-1
2x-3=10^(y-1)
x=[10^(y-1(+3]/2
反函数y=[10^(x-1)+3]/2