Find the domains of definaton of the following functions:
(a) `f(x)=sqrt(x-1)+sqrt(6-x)`
(b) `f(x)=sqrt(x^2-x-2)+(1)/sqrt(3+2x-x^(2))`
(c) `f(x)=(x)/sqrt((x^(2)-x-2))`
(d) `f(x)=sqrt(sin x-1)`
(e) `f(x)=sqrt(log""(5x-x^(2))/(4))`,
(f) `f(x)=log_(x) 5,`
(g) `f(x)=log ""(x^(2)-5x+6)/(x^2+4x+6)`
(h) `f(x)=arc sin ""(x-3)/2-log(4-x)`
(i) `f(x)=(1)/(log(1-x))+sqrt(x+2),`
(j) `f(x)=log cos x,`
(k)`f(x)=arc cos ""(3)/(4+2 sin x)`
(l) `y=(1)/sqrt(|x|-x)`

Answer

(b) (2,3) (c) `(-oo,1) and (2,oo)` (d) `x=pi/2+2kpi (k =0, pm 1, pm2,....)`