plz help urgent. Calculus

Question

√(x + 1/x-1) , and g(x)=lnx

a) determine the domains and ranges of these functions;

b) find formulas for (f◦g)(x) and (g◦f) (x) ;

c) find the domain of the composite functions of part(b).

Answer 1

f(x) = sqr((x+1)/(x-1))

g(x) = lnx

domain of f(x) is all real numbers except those that make the denominator =0 or make the square root imaginary, which is x=1 and (x+1)/(x-1)<0, x<-1

or in interval notation x is not in the interval (-infinity, -1)U{1}

x is in the intervals [-1,1)U(1,infinity)

range of f(x) is [0, infinity) or x>/=0

domain of g(x) is x>0 or x is in the interval (0, infinity)

range of g(x) is all real numbers

f(g(x)) = f(lnx) = sqr((lnx+1)/(lnx-1))

g(f(x)) =g(sqr((x+1)/(x-1))) = ln(sqr((x+1)/(x-1)))

domain of f(g(x)) is the interval (0, infinity), when x>0, same as the domain of g(x)

domain of g(f(x)) = almost the same as domain of f(x), but f(x) can't = 0

which is the interval (-1,1)U(1,infinity)

it may help to use a graphing calculator on the functions