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y=3^(x-1)+2
y-2=3^(x-1)
x-1=log3(y-2)
x=log3(y-2)+1
X and Y exchange
The inverse function is y = log3 (X-2) + 1

Inverse function of y = 1 / 3 * 2 ^ (x-1)

Find the inverse function, directly change y into x, X change y, and then simplify
y=1/3*2^(x-1)
x=1/3*2^(y-1)
y=log2(3x) + 1

Inverse function y = √ (e ^ x + 1)

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Y = (e ^ x) - 1 (x belongs to R, Y > - 1), e ^ x = y + 1, x = ln (y + 1)
Therefore, the inverse function of y = (e ^ x) - 1 (x belongs to R) is y = ln (x + 1) (x > - 1)

How to do the inverse function of y = 1-e ^ x

y=1-e^x
Swap x, y
x=1-e^y
e^y=1-x
Take logarithm on both sides
y=ln(1-x) (x

Inverse function y = (E ＾ x + 1) / (E ＾ x)

y=(e＾x+1)/(e＾x)
=1+e＾(-x) ＞1
e＾(-x) =y-1
-x=ln(y-1)
x=-ln(y-1)
=ln(x-1)^(-1)
The inverse function: y = ln (x-1) ^ (- 1) (x > 1)

What is the inverse function of y = e ^ X / e ^ x + 1

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y=（a-x）/（1+x）
y+xy=a-x
y-a=-x-xy
(y-a)/(-1-y)=x

Y = 2x-3 / 5x + 1 (x belongs to R, and X is not equal to - 1 / 5)

Y = (2x-3) / (5x + 1) 5xy + y = 2x-3 y + 3 = 2x-5xy = x (2-5y) x = (y + 3) / (2-5y) the inverse function is y = (x + 3) / (2-5x). (x is not equal to 2 / 5). Thank you for your adoption~~

F (x) = 2x / 5x + 1 inverse function y (5x + 1) = 2x

y(5x + 1) = 2x
5xy + y = 2x
2x - 5xy = y
x(2 - 5y) = y
x = y/(2 - 5y)