Question

Given `f(x)=sqrt(7x+7)` and `g(x)=1/x`, how do you find `(f/g)(x)`?

Answer 1

See below.

Explanation:

Given `f(x)=sqrt(7x+7)` and `g(x)=1/x`, you can find the quotient of the two functions:

`(f/g)(x)=(sqrt(7x+7))/(1/x)`

When we divide fractions, we know that `a/b -: c/d`, written `(a/b)/(c/d)` is equivalent to `a/b xx d/c`. We can apply this to our rational function. In the numerator, we have `(sqrt(7x+1))/1` and in the denominator, `1/x`.

`=>(sqrt(7x+1))/1 xx x/1`

`=>xsqrt(7x+7)`

You could also factor out `7` from inside the radical and write the answer as:

`xsqrt(7(x+1))`