Question

If f(x)=(x+1)^−1 and g(x)=x−2, what is the domain of f(x)÷g(x)?
A) all values of x
B) (−∞,−1),(−1,2), and (2,∞)
C) (−∞,2) and (2,∞)
D) (−∞,−1] and [2,∞)

i don't quite understand how to get the answer. help plz.

Answer 1

first set up f(x)/g(x)

Answer 2

f(x)=1/(1+x) /(g(x)
dividing by g(x) is the same as times by reciprocal .

Answer 3

so instead of (x+1)^-1/ x-2, it would be x-2*(x+1)^-1

Answer 4

Yes,
1/ploynomial means there will be an asymtote

Answer 5

well,
\(\large\color{black}{ \displaystyle f(x)=(x+1)^{-1} }\)
\(\large\color{black}{ \displaystyle g(x)=x-2 }\)

then, \(\large\color{black}{ \displaystyle \frac{f(x)}{g(x)}~~~~\Rightarrow~~~~\frac{(x+1)^{-1}}{x-2} }\)

Answer 6

but that is then same as
\(\large\color{black}{ \displaystyle \frac{f}{g}(x)~~=~~\frac{1}{(x-1)(x-2)} }\)

Answer 7

so there are 2 values at which the function is undefined ... what are they?

Answer 8

in a factored equation like (x+1)*(x-2)
the places where it would cross the x axis would be -1 and +2.
when you do 1/(poly) , those points become the asymtotes.