Question

answers with procedure

Answer 1

11) given,

the domain of log (x³-x) :

f(x) is defined for x³-x>0 because if x³-x = 0

then the value of log0 is not defined.

x³-x>0 => x(x²-1)>0 => x(x-1)(x+1)>0

So Domain = (-1,0) U (1, infinity)

12) given,

f(x) is defined when (x-2)>0 and (3-x)>0

=> (x-2)>0 and (x-3)<0

=> x>2 and x<3

Domain = (2,3)

1) given,

f(x) is defined [x]²-[x]-6>0

=>[x]²-3[x]+2[x]-6>0

=>[x] ([x]-3) +2 ([x]-3)>0

=>([x]-3) ([x]+2) >0

=>[x]<-2 and [x]>3

=>x<-2 and x≥4

so Domain = (-infinity,2) U [4, infinity)

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