Let f (x) = The square root of (x-1) and g(x)= x^2 . Find the domain of the composite function (f ◦g) = f (g(x)).

Question

xapproachesinfinity · Answer

f(g(x)
x====>g(x)=====>f(g(x))
domain of f(g(x)) is the range of g(x)
so $g(x)-1\geq0 \Longrightarrow  x^2-1\geq0\Longrightarrow  (x-1)(x+1)\geq0$
so you can only allow $(-\infty, -1]\cup[1,\infty)$

xapproachesinfinity · Answer

ask yourself what are the set of numbers i can allow in the radical
of the the set of the range of g(x) (which is the domain of the composite f(g(x)))

anonymous · Answer

Thank you so much, that was what I thought, just could not figure out how to put it down on paper... Thank you again!

xapproachesinfinity · Answer

welcome^_^
i hope that helped you to understand how the composite functions work
you just consider the range of the inside function and see what can you allow

anonymous · Answer

Yes, It verified what I thought, just was not sure... Thank you again! ^_^