Question

For f(x) = 4x +1 and g(x) = x2 - 5, find (g/f) (x).

Answer 1

`\left(g/f\right)\left(x\right)=(x)/(4)-(1)/(16)-(79)/(16\left(4x+1\right))`

Explanation:

`f(x)=4x+1`

`g\left(x\right)=x^2\:-\:5`

As

(g/f)(x) = g(x) / f(x)

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

`=(x)/(4)+(-(x)/(4)-5)/(4x+1)`

`=(x)/(4)-(1)/(16)+(-(79)/(16))/(4x+1)`

`=(x)/(4)-(1)/(16)-(79)/(16\left(4x+1\right))`

Therefore,

`\left(g/f\right)\left(x\right)=(x)/(4)-(1)/(16)-(79)/(16\left(4x+1\right))`