The inverse function of y = 1 + LG (x + 3) is

The inverse function of y = 1 + LG (x + 3) is

0

y=lg(1-2x),x

X1,
y=lg(1-2x)>0,
10^y=1-2x,
2x=1-10^y,
x=1/2-1/2·10^y .
y=1/2-1/2·10^x,x>0.

Definition domain of inverse function of y = 2x-1 / 2x + 1

The definition domain of inverse function is the range of original function
y=(2x2-1)/(2x2+1)
X2=(y+1)/(2-2y)≥0
The result is - 1 ≤ y

Definition domain of inverse function of y = 2x-1 / 2x + 1

0

0

X + √ (x ^ 2-1) = 10 ^ y, t = 10 ^ y
√(x^2-1)=t-x
Square: x ^ 2-1 = T ^ 2-2tx + x ^ 2
X = (T ^ 2 + 1) / (2t)
That is, x = (100 ^ y + 1) / (2 * 10 ^ y)
Exchange x, y to get the inverse function: y = (100 ^ x + 1) / (2 * 10 ^ x)

Find the inverse function of y = x 2 + 1 (x ≥ 0); y = 2x + 1 (x < 0)

The first, y = radical X-1,
The second, y = (x-1) / 2

y=2X+3/X-1 (X

0

0

y=lg(x^2+2x) x^2+2x=10^y (x+1)^2=10^y+1 x=√ (10^y+1)-1 Y=√ (10^X+1)-1
Adopt it

Find the inverse function y = lgx + LG (x + 2) As the title ~

The mistake upstairs is bizarre
y=lg(x^2+2x)
be
10^y=x^2+2x
Add 1 on both sides at the same time
10^y+1=x^2+2x+1=(x+1)^2
X + 1 = positive and negative root sign (10 ^ y + 1)
That is, x = positive and negative root sign (10 ^ y + 1) - 1
So the inverse function is
Y = positive and negative root sign (10 ^ x + 1) - 1
It can be seen from the original function that the image of this function is two segments, so the inverse function should also be two segments

The inverse function of the function y = LG (x + 1) is an important process

y=lg(x+1)
x+1=10^y
x=10^y-1
So the inverse function is y = (10 ^ x) - 1