Question

For f(x)=4x+1 and g(x)=x^2-5 find (g/f)(x)

Answer 1

`((g)/(f))(x)=(x^2-5)/(4x+1)`

Explanation:

We have been given two function formulas
`f(x)=4x+1` and
`g(x)=x^2-5`.

By the definition of composition
`((g)/(f))(x)=(g(x))/(f(x))`.

Upon substituting our given values we will get,

`((g)/(f))(x)=(x^2-5)/(4x+1)`

Since we can not simplify our expression further, therefore,
`((g)/(f))(x)=(x^2-5)/(4x+1)`.

Answer 2

`f(x)=4x+1\\\\g(x)=x^2-5\\\\(g/f)(x)=(g(x))/(f(x))=(x^2-5)/(4x+1)`