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

Question

Eva Adamson · Accepted Answer

See below.

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))#

Eva Adamson · Answer

undefined To find (f/g)(x), you divide the function f(x) by the function g(x). So, (f/g)(x) = f(x) / g(x). Substituting the given functions, f(x) = √(7x + 7) and g(x) = 1/x, into the equation, we have:

(f/g)(x) = √(7x + 7) / (1/x)

To simplify, multiply the numerator and denominator by x:

(f/g)(x) = x√(7x + 7) / 1

Therefore, (f/g)(x) = x√(7x + 7).