a)state the largest domain of each functions
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
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.