Question

do the question of attachment-​

Answer 1

Simple question

The concept of domain says that,the no. with log can never be less than 0,so

1-x>0

x<1.....ii)

this is the first condition

now we also, know that no. in root should never be less than 0

so,

x^2-1>=0 (>= means gretaer than or equal to)

(x+1)(x-1)>=0....... ii)

Now we will draw a number line,to find the value of x ,which satisfy the given condition

Take 1 -1 on the number line

put x=2 we get

(x+1)(x-1)=3,which is positive,so number after 1 will be positive

putting x=1/2 we get

(x+1)(x-1)=(1/2 +1)(1/2 -1)=-3/4

so,number between 1 and -1 will be negative

now alternatively,we will can draw the number line

the value will be positive,if x belongs to (-inf,-1],[1,infi)

but if we see the first condition,,,then we have to neglect [1,inf)

hence the domain will be(-inf,-1]