Question

Question #45820

Answer 1

`(f*g)(x)=log(x+1)/(x-2)`, `x` `in(-1,2)uu(2,+oo)`

Explanation:

`*` `f(x)=1/(x-2)`

`x-2!=0` `<=>` `x!=2`

so `Df=R-{2}` = `(-oo,2)uu(2,+oo)`

`*` `g(x)=log(x+1)`

`x+1>0` `<=>x> -1`
so `Dg=(-1,+oo)`

For `x` `in` `DfnnDg` `=` `(-1,2)uu(2,+oo)`
`(f*g)(x)` `=` `f(x)*g(x)=1/(x-2)*log(x+1)` `=log(x+1)/(x-2)`