Question

For f(x)=2x+1 and g(x)=x^2-7, find (g/f)(x)

Answer 1

g(f(x))=g(2x+1)= (2x+1)∧2-7=4x∧2+4x+1-7=4x∧2+4x-6

Good luck!!!

Answer 2

`((g)/(f))(x)=(x^2-7)/(2x+1)`.

Explanation:

We have been given two functions as:
`f(x)=2x+1\text{ and } g(x)=x^2-7`. We are asked to find
`((g)/(f))(x)`.

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

Upon substituting
`f(x)=2x+1\text{ and } g(x)=x^2-7` in our equation, we will get:

`((g)/(f))(x)=(x^2-7)/(2x+1)`

We cannot further simplify our given equation, therefore,
`((g)/(f))(x)=(x^2-7)/(2x+1)` would be our answer.