[tex]f(x)=4x+1\\\\g(x)=x^2-5\\\\(g/f)(x)=\dfrac{g(x)}{f(x)}=\dfrac{x^2-5}{4x+1}[/tex]
Answer:
[tex](\frac{g}{f})(x)=\frac{x^2-5}{4x+1}[/tex]
Step-by-step explanation:
We have been given two function formulas [tex]f(x)=4x+1[/tex] and [tex]g(x)=x^2-5[/tex].
By the definition of composition [tex](\frac{g}{f})(x)=\frac{g(x)}{f(x)}[/tex].
Upon substituting our given values we will get,
[tex](\frac{g}{f})(x)=\frac{x^2-5}{4x+1}[/tex]
Since we can not simplify our expression further, therefore, [tex](\frac{g}{f})(x)=\frac{x^2-5}{4x+1}[/tex].
