Question

Let `f(x)=x^2-4` and `g(x)=4x`, how do you find `(f/g)(x)`?

Answer 1

See explanation.

Explanation:

To find such a function you have to write an expression using the given operations with the formulas of functions `f` and `g` as arguments:

`(f/g)(x)=(x^2-4)/(4x)`

The next step is finding the domain of new function.

Both `f` and `g` are polynomials therfore are defined for all real numbers, however in `(f/g)` `g(x)` appears in the denominator. This excludes all zeros of `g(x)` from the domain. So `(f/g)` is defined for `x in RR-{0}`