Question

Hi! I really need help with these. I tried them on my own but I got really confused. Thanks!


1.) If f(x)=1/x and g(x)=1/x^2, find the domain of g/f


2.) If h(x)=4/(5x+2)^2, find the two functions f and g so that f(g(x))=h(x).

Answer 1

1. keep in mind that both f(x) and g(x) would be undefined for x=0
so even though g/f = (1/x) / (1/x^2) = x
the final function would still be undefined (actually it would be indeterminate) for x = 0

so the domain is :
set of all real numbers, x ≠ 0

Answer 2

183.79