The domain of y=lg( 1-x) satisfies {x | 1-x > 0},

Solution: {x | x < 1}.

So the domain of the function y=lg( 1-x) is (-∞, 1).

The domain of logarithmic function y=logax is {x | x >；; 0}, but if you encounter the solution of the domain of logarithmic compound function, you should not only pay attention to greater than 0, but also pay attention to the fact that cardinality greater than 0 is not equal to 1.

If the domain of function y=logx(2x- 1) is required, it needs to satisfy x >；; 0 and x≠ 1 and 2x-1>; 0, get x> 1/2 and x≠ 1, that is, its domain is {x | x >；; 1/2 and x≠ 1}.

Extended data

Basic operating rules

If p > is known; 0, Q>0, a> 1 or 0.

1, real number multiplication

LogaPQ=logaP+logaQ, simple memory is that the multiplication of real numbers equals the addition of logarithm.

2. Real number division

LogaP/Q=logaP-logaQ, simple memory is that the division of real numbers equals the subtraction of logarithm.

3. The power of real numbers

logaP^n=n*logaP

4, the strength of the base

loga^mP= 1/m*(logaP)

5. Both real numbers and radix contain power operation.

loga^mP^n=n/m*(logaP)

6. Base substitution method

LogaP=(log2P)/(log2a), that is, the solution of the number can be changed into another form of division of the logarithm with the same base, and the logarithm can be changed into anyone or according to the needs of calculation. The true number is above and the radix is below.