Question

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

Answer 1

Answer:

$\left(g/f\right)\left(x\right)=\frac{x}{4}-\frac{1}{16}-\frac{79}{16\left(4x+1\right)}$

Step-by-step explanation:

$f(x)=4x+1$

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

As

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

            $=\:\frac{x^2\:-\:5}{4x+1}\:\:\:\:\:\:$

            $=\frac{x}{4}+\frac{-\frac{x}{4}-5}{4x+1}$

              $=\frac{x}{4}-\frac{1}{16}+\frac{-\frac{79}{16}}{4x+1}$

               $=\frac{x}{4}-\frac{1}{16}-\frac{79}{16\left(4x+1\right)}$

Therefore,

$\left(g/f\right)\left(x\right)=\frac{x}{4}-\frac{1}{16}-\frac{79}{16\left(4x+1\right)}$