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

1 Answer
Dec 29, 2016

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))#