Answer:
[tex](\frac{g}{f})(x)=\frac{x^2-7}{2x+1}[/tex].
Step-by-step explanation:
We have been given two functions as: [tex]f(x)=2x+1\text{ and } g(x)=x^2-7[/tex]. We are asked to find [tex](\frac{g}{f})(x)[/tex].
By the definition of composite function [tex](\frac{g}{f})(x)=\frac{g(x)}{f(x)}[/tex].
Upon substituting [tex]f(x)=2x+1\text{ and } g(x)=x^2-7[/tex] in our equation, we will get:
[tex](\frac{g}{f})(x)=\frac{x^2-7}{2x+1}[/tex]
We cannot further simplify our given equation, therefore, [tex](\frac{g}{f})(x)=\frac{x^2-7}{2x+1}[/tex] would be our answer.
