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,∞)

Answer 1

the answer is b

Explanation:

Answer 2

`a^(-1)=(1)/(a)\\\\\text{therefore:}\\\\f(x)=(x+1)^(-1)=(1)/(x+1)`

`g(x)=x-2`

`f(x)/ g(x)=(1)/(x+1)/(x-2)=(1)/(x+1)\cdot(1)/(x-2)=(1)/((x+1)(x-2))\\\\\text{The domain:}\\\\(x+1)(x-2)\\eq0\iff x+1\\eq0\ \wedge\ x-2\\eq0\\\\x\\eq-1\ \wedge\ x\\eq2`

`\text{Therefore your answer is B.}\\(-\infty;-1)\ \cup\ (-1;\ 2)\ \cup\ (2;\ \infty)`