Julia L. answered • 05/29/20
University Student Pursuing Minor in Math
Hi! To answer this, first consider how f(g(x)) is the same as plugging g(x) (which is √(1-x)) into f(x).
So, substitute √(1-x) in for x in f(x) = x2 - 2x.
Once you have simplified out f(g(x)), finding the domain is much simpler. The domain of f(x) (EDIT: or any function, such as g(x) or f(g(x)) ) shows which values of x are allowed to be plugged into f(x). So, if a value of x results in dividing by 0 or taking the square root of a negative number, it is not part of the domain.
To find the domain of a function with square roots, set everything under the square root to be ≥ 0 and solve for x. This will find you all the inputs into the function that ensure that the square root of a negative is never taken.
Julia L.
To make it easier to see the domain, try graphing f(g(x)). The domain will be the x-range. Try again to see what values of x cause f(g(x)) to cause an error (such as taking the square root of a negative).05/29/20
Grace M.
Just to check then, is f(g(x)) x-1 -2(sq rt 1-x)?05/29/20
Julia L.
I would check the first part again when you did (sqrt(1-x))^2.05/30/20
Grace M.
Is the domain (negative infiniti, positive infiniti)?05/29/20