Answer
Domain for $ f(x)$: $(-\infty,\infty)$, Range for $ f(x)$: 2
Domain for $ g(x)$: $(-\infty,\infty)$, Range for $ g(x)$: $[1,\infty)$
Domain for $ f(x)/g(x)$: $(-\infty,\infty)$, Range for $ f(x)/g(x)$: $(0,2]$
Domain for $ g(x)/f(x)$: $(-\infty,\infty)$, Range for $ g(x)/f(x)$: $[\frac{1}{2},\infty)$
Work Step by Step
The domain is all the values that $x$ can take on. Typically, for polynomials, the domain is all real numbers. If there are square roots or other even-numbered roots, we must make sure that negative values inside the root are excluded. If fractions exist, we must make sure that there is no zero in the denominator.
The range is all the values that $y$ can take on. This can easily be seen by graphing the function.
For our functions, the domains are all real numbers and the ranges can be found by graphing.
