Answer:
Given functions,
Since, by the compositions of functions,
1. (g◦f)(x) = g(f(x))
Since, (g◦f) is defined,
If 3 - x² ≥ 0
⇒ 3 ≥ x²
⇒ -√3 ≤ x ≤ √3
Thus, Domain = [-√3, √3]
2. (f◦g)(x) = f(g(x))
Since, (g◦f) is defined,
If x ≥ 0
Thus, Domain = [0, ∞)
3. (f◦f)(x) = f(f(x))
Since, (f◦f) is a polynomial,
We know that,
A polynomial is defined for all real value of x,
Thus, Domain = (-∞, ∞)
Answer:
25 minutes
Step-by-step explanation:
Let the amount of time, in minutes, be x.
For Container A, we can write:
200 + 6x [since it has 200 and is being filled with 6 per minute]
For Container B, we can write:
500 - 6x [since it has 500 and is being drained with 6 per minute]
To find, we equate them and solve for x:
<em>So, in 25 minutes (m), the two containers will have same amount of water</em>