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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,∞)

Respuesta :

gmany

[tex]a^{-1}=\dfrac{1}{a}\\\\\text{therefore:}\\\\f(x)=(x+1)^{-1}=\dfrac{1}{x+1}[/tex]


[tex]g(x)=x-2[/tex]



[tex] f(x)\div g(x)=\dfrac{1}{x+1}\div(x-2)=\dfrac{1}{x+1}\cdot\dfrac{1}{x-2}=\dfrac{1}{(x+1)(x-2)}\\\\\text{The domain:}\\\\(x+1)(x-2)\neq0\iff x+1\neq0\ \wedge\ x-2\neq0\\\\x\neq-1\ \wedge\ x\neq2 [/tex]


[tex]\text{Therefore your answer is B.}\\(-\infty;-1)\ \cup\ (-1;\ 2)\ \cup\ (2;\ \infty)[/tex]

Answer:

the answer is b

Step-by-step explanation: