Question

Please help :( 2 questions..

If c(x)=5/x-2 and d(x)=x+3 what is the domain of (cd)(x)?

And, if f(x)=7+4x and g(x)=1/2x, what is the value of (f/g)(5)?,

Answer 1

I just took the test for the first question its all real values of x except x=2. I got it right. And i believe the answer to the second one is 270. Hope this helps! Good luck (:

Answer 2

First note that since there are no parantheses in c, then c(x)=(5/x)-2. If c(x)=(5/x)-2 and d(x)=x+3, then (cd)(x) means multiply c(x)*d(x). c(x)*d(x)=[(5/x)-2]*(x+3). We multiply each term by each term and we get (5/x)*x-2*x+3*(5/x)-2*3=(5/x)(x/1)-2x+(3/1)(5/x)-6=5-2x+(15/x)-6. Since we have an x in the denominator, it cannot be 0. There are no other restrictions except x cannot be 0. SO the domain is (-infinity,0)U(0,infinity) or All Real numbers except x=0. For (f/g)(5), f(5)=7+4*5=27 and g(5)=(1/2)(5)=(5/2). (f/g)(5)=f(5)/g(5)=27/(5/2) and by inverting and multiplying we get 27*(2/5)=54/5.