Question

2.0 + 10 3x + 12 Given f(x) and g(x) f(x) find the domain of g(x) - 3 - 2 x + 4 The domain is all real numbers except x = Submit Question

Answer 1

The domain of the quotient between the two functions is the intersection of the domain of each individual function, except the points where g(x)=0.

In any case, the denominator must be different from 0.

The domain of f is the set of all real numbers except x=-2, since:

`x=-2\Rightarrow-x-2=-(-2)-2=2-2=0`

The domain of g is the set of all real numbers except x=-4. This can be proven using a similar procedure.

On the other hand, g(x)=0 whenever x=4.

Therefore, the domain of f(x)/g(x) is the set of all real numbers, except:

`\begin{gathered} x=-2 \\ x=4 \\ x=-4 \end{gathered}`