SOLUTION: State the domain: g(x)= 2x+1 over x-7

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Question 206433: State the domain: g(x)= 2x+1 over x-7
Found 2 solutions by dyakobovitch, mickclns:
Answer by dyakobovitch(40) About Me  (Show Source):
You can put this solution on YOUR website!
g(x) = (2x+1)/(x-7). The domain is all values of x that make an output (y) possible. All values of X are in the domain, except when the equation is undefined. The rational expression will be undefined when you divide by 0. As such, x-7 is not equal to 0. Therefore, x is not equal to 7.

So your domain is D={x|x is not equal to 7} ... or (- infinity,7) U (7, infinity).

Feel free to leave any comments or concerns. -- David

Answer by mickclns(59) About Me  (Show Source):
You can put this solution on YOUR website!
A graph of +%282x%2B1%29+%2F+%28x-7%29+ is +graph%28400%2C200%2C-70%2C25%2C-17%2C20%2C++%282x%2B1%29+%2F+%28x-7%29+%29+
As x gets larger and larger positively or negatively, y will exist (so x will also) and will get close to 2. However, as x gets closer and closer to 7 the numerator gets closer and closer to 15, but the denominator gets closer and closer to 0, meaning the denominator is tinier and tinier. But, if you take a number near 15 and divide by a tiny number you get a large (+ or -) number. For instance, if x = 6.99 then the numerator is 14.98 and the denominator is -0.01 which is the same as -1/100.
So, +g%286.99%29+=+14.98%2F-0.01+=+14.98%2A-100+=-1498+ which is a huge number, way off the bottom of the graph and +g%287.01%29+=+15.02%2F0.01+=+15.02%2A100+=1502 which is a huge number, way off the top of the graph.
Speaking of the graph, near to x = 7, you can see part of the graph that is a vertical line. That shouldn't actually be there. Near to 7 the actual graph just continues farther and farther off the bottom and top of the picture with nothing in the middle (in the picture, where x very near to 7). If x = 7 then g(7) is 15 / 0, but, since you can't divide by 0, g(7) does not exist, so 7 is not in the domain of g. All this is to say that the domain of g is ALL REAL NUMBERS EXCEPT FOR 7.
- Mick