Question

Find (f/g)(x) when f(x)=3x+2 and g(x)=5x-6

Answer 1

We have this two functions:

`\begin{gathered} f(x)=3x+2 \\ g(x)=5x-6 \end{gathered}`

We have to calculate what f/g is.

`((f)/(g))(x)=(f(x))/(g(x))=(3x+2)/(5x-6)`

What is the domain of (f/g)(x)?

The domain is all the values of x for which the function has a defined value.

That means that if the denominator becames 0, the function is not defined.

This happens when 5x-6=0:

`\begin{gathered} 5x-6=0 \\ 5x=6 \\ x=(6)/(5) \end{gathered}`

Then, the domain is "all the real numbers different from 5/6".