Question

(Simplify your answers completely.)

=1
f(x)=x+1 g(x) =
(a) (f+g)(x) =
1'
(b) (f-g)(x) =
(c) (fg)(x) =
(d) (f/g)(x)
=
What is the domain of f/g? (Enter your answer using in

Answer 1

Hi,

Explanation:

`f(x)=(x)/(x+1) \\g(x)=(1)/(x^4)\\`

`(a) \ (f+g)(x)=f(x)+g(x)=(x)/(x+1)+(1)/(x^4)=(x^5+x+1)/(x^4(x+1))`

`(b) \ (f-g)(x)=f(x)-g(x)=(x)/(x+1)-(1)/(x^4)=(x^5-x-1)/(x^4(x+1))\\`

`(c) \ (f.g)(x)=f(x).g(x)=(x)/(x+1).(1)/(x^4)=(1)/(x^3(x+1))\\`

`(d) \ (f/g)(x)=f(x)/g(x)=((x)/(x+1))/((1)/(x^4))=(x)/(x+1) *(x^4)/(1)=(x^5)/(x+1)\\`

`dom\ ((f/g)(x))=\mathbb{R}-\{-1\}=]-\infty,-1[\ \cup\ ]-1,\infty[\\`