a)state the largest domain of each functions

Question

f:x=1/x^2-1 and g:x=x/x+2
where x is a real number
b)find:
i)the inverse function of g^-1 of g
ii)the composite function g^-1(f(x)).In each case state largest domain

Answer 1

of the function.

a)The largest domain of f is all real numbers, and the largest domain of g is all real numbers except for x=-2.

b)i)The inverse function of g is g^-1(x)=2x/(x-1). The largest domain of g^-1 is all real numbers except for x=1.

ii)The composite function g^-1(f(x))=2/(1/x^2-1)-2. The largest domain of this function is all real numbers except for x=0 and x=-1.

Answer 2

g^-1(f(x)) = 2f/(f-1) = (2*1/(x^2-1)) / (1/(x^2-1) - 1) = 2/(2-x^2)