Answer:
1. (-4,6) there is no a solution to the equation through this point
2. (2,−6) there is no a solution to the equation through this point
3. (−5,39) there is a solution to the equation through this point
4. (−1,45) there is a solution to the equation through this point
Step-by-step explanation:
Using the existence and uniqueness theorem:
Let:
Now, let's find the domain of , due to the square root:
So the domain of the function is:
Now, due to the fraction the denominator must be also different from 0, so:
So, the theorem tells us that for each there exists a unique solution defined in an open interval around .
1. (-4,6) there is no a solution to the equation through this point because
2. (2,−6) there is no a solution to the equation through this point because
3. (−5,39) there is a solution to the equation through this point because
4. (−1,45) there is a solution to the equation through this point because