If f(x)=(x+1)^−1 and g(x)=x−2, what is the domain of f(x)÷g(x)?

Question

campbell_st · Answer

well rewrite it as 

$$f(x) = \frac{1}{x + 1}$$

then if you divide by g(x) its 

$$\frac{1}{(x + 1)} \div (x -2)~~~or  ~~~\frac{1}{x +1} \times \frac{1}{x -2}$$

so the domain is all real x, except there are 2 excepts.... you need to find them....

anonymous · Answer

(−∞,−1] and [2,∞)?

anonymous · Answer

@campbell_st

campbell_st · Answer

well you have the correct values for the exclusions.... 

but if you look at the domain you stated, you could have x = 0.... 

so I'd say all real x, except $$x \neq -1 or 2$$

anonymous · Answer

i have the answer choice "all values of x"  , (∞,−1),(−1,2), and (2,∞) , (−∞,2) and (2,∞) , & (−∞,−1] and [2,∞)

campbell_st · Answer

so looking at the problem... things don't match my thinking... 

as x = 1 is aslo between the values x = -1 and x = 2

substitute x = 1 and you still get a numerical value... 

so I'll let someone else who is smarter help you.

anonymous · Answer

That's okay, I appreciate your help anyways

anonymous · Answer

How about "If f(x)=2x^2−x−6 and g(x)=x^2−4, what's f(x)÷g(x)?

campbell_st · Answer

here is a graph of the curves...

campbell_st · Answer

well for this question... its simple, start by factoring

$$\frac{2x^2 - x - 6}{x^2 - 4} = \frac{(2x + 3)(x - 2)}{(x +2)(x-2)}$$

and hopefully you can finish it from here.

anonymous · Answer

Thanks!