Answer:
A
Step-by-step explanation:
You can eliminate B and D because it’s using [tex]\frac{g}{f}[/tex], but the question is asking [tex]\frac{f}{g}[/tex]. So it’s either A or C. They are both written correctly, but out of the two, A is correct because just that x ≠ [tex]\sqrt{7}[/tex] part of it is what makes it true.
The reason being is that the only thing that won’t make [tex]\frac{2x+1}{x^{2}-7 }[/tex] true is when the denominator equals 0, because anything divided by 0 is undefined. So, when you plug [tex]\sqrt{7}[/tex] for x in the denominator you get: [tex]\sqrt{7^{2} } -7[/tex]. The [tex]\sqrt{7^{2} }[/tex] part just turns into 7, and 7 - 7 is 0. So you don’t want x to equal [tex]\sqrt{7}[/tex].
So the answer is A: [tex]\frac{2x+1}{x^{2}-7}[/tex], [tex]x\neq[/tex] ± [tex]\sqrt{7}[/tex]
There you go my friend!
I hope you understand and that this helps with your question! :)
