Question

Let f(x) = −x^2 and g(x) = 1/√x. Find formulas for f ◦g and g◦f and state the domain of each composition. I only need the domains if possible.

Answer 1

Answer: see below

Explanation:

`f(x)=-x^2\qquad g(x)=(1)/(\sqrt x)`

`f og(x)=f\bigg((1)/(\sqrt x)\bigg)\\\\.\qquad =-\bigg((1)/(\sqrt x)\bigg)^2\quad \\\\.\qquad =-(1)/(x)\\\\\text{Domain:}\ x>0`

`gof(x)=g(-x^2)\\\\.\qquad =(1)/(√(-x^2))\\\\.\qquad =(1)/(xi)\\\\\text{Domain: Does Not Exist since result is an imaginary number}`