Question

For the pair of function f and g, determine the domain of f/g.f(x)=2x-3, g(x)= 3x-6

Answer 1

The given functions are

`\begin{gathered} f(x)=2x-3 \\ g(x)=3x-6 \end{gathered}`

Let's find the quotient between these functions

`(f(x))/(g(x))=(2x-3)/(3x-6)`

The domain of this new function is determined by the denominator 3x-6 because it can't be equal to zero.

`3x-6\\e0`

Let's solve for x

`\begin{gathered} 3x-6\\e0 \\ 3x\\e6 \\ x\\e(6)/(3) \\ x\\e2 \end{gathered}`

This means the domain must have a restriction.

Therefore, the domain would be

`D\colon\mleft\lbrace x|x\in\R/x\\e2\mright\rbrace`

In words, the domain of the function is all real numbers except the number 2.