Answer:Definition area"? Do you mean the "natural domain" of the function- the region in which the formula is defined? In order that a number have a square root that number must be non-zero.
Step-by-step explanation:Here, we must have x−1x≥0.
If x is positive, multiplying both sides by x we have x2−1=(x−1)(x+1)≥0. In order for that to be true, both x- 1 and x+ 1 must have the same sign: either x-1> 0 and x+ 1> 0 or x- 1< 0 and x+ 1< 0. The first pair of inequalities is true for x> 1 and the second for x< -1. Since "x is positive", we must have x> 1.
If x is negative, multiplying both sides by x we have x2−1=(x−1)(x+1)≥0. In order for that to be true, x- 1 and x+ 1 must have opposite signs: x+ 1> 0 and x- 1< 0 or x- 1<0 and x- 1> 0. The first pair is true for −1≤0≤1. The second pair are never both true. Since "x is negative" we must have −1≤x≤0.
Of course, we also cannot divide by 0 so x= 0 is not in the domain. The domain is the union of the two separate sets:{x|−1≤x<0}∪{x|x>1}.
Hope That Helps!
D because you can’t put a negative over a exponent
Answer:
{-5/4, 8}
Step-by-step explanation:
We are given (4u + 5)(8 - u) = 0. Solve for u by setting each of the factors (4u + 5) and (8 - u) equal to zero and solving each of the resulting equations:
4u + 5 = 0 leads to u = -5/4, and
8 - u = 0 leads to u = 8.
The solutions are {-5/4, 8}
2(x-7)-10=12-4x
2x-14-10=12-4x
2x-24=12-4x
2x-12=-4x
-12=-2x
6=x
