Find the domain, intercepts, and any symmetry?

Question

If f(x) = 1/(sq.root x) and g(x) = x^2-3, then find h(x) = f(g(x))

A.) Find the Domain

B.) Give all intercepts

C.) Describe any symmetry

Answer 1

hi

h(x)=f(g(x))=1/(sqr(x^2-3))

D  :: x^2-3>0

    then  x>3 OR x<-3

Answer 2

A)  dom f: x>0,   dom g: all reals,   dom h: x>0

B)   f: none.     g:  (sqrt(3),0),(-sqrt(3),0),(0,-3), h: none

C)    f: none,    g: y-axis symmetry,     h:    y-axis symmetry