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

Question 206433: State the domain: g(x)= 2x+1 over x-7
Found 2 solutions by dyakobovitch, mickclns:
Answer by dyakobovitch(40) (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) (Show Source): You can put this solution on YOUR website!
A graph of is
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, which is a huge number, way off the bottom of the graph and 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
RELATED QUESTIONS
State the domain of the following: g(x)=2x+1/x-3 (answered by MathLover1)
Hello can someone please try and solve these problems, i would greatly appericiate it!! (answered by MathLover1)
f(x)= 1/x-1; g(x)= √x find f(g(g)) and g(f(g)). State the... (answered by stanbon)
State the domain and range of each function.... g(x)=ln(2x-1)... (answered by jsmallt9)
State the domain of the following Question 1 a) f(x)=suareroot x+4 b) g(x)=... (answered by stanbon,Nate)
state the domain of the composite function. f(x)=x^2+1;... (answered by stanbon)
1. For a given functions f and g, find the requested function and state its domain.... (answered by robertb)
Perform the operation and state the domain and range of g(f(x)) f(x)= x^2+3x; g(x)=... (answered by Fombitz)
find the domain of (h/g)(x), given that h(x)=5x/(3x-7) and g(x)=(x^4-1)/(5x-15). State... (answered by stanbon)