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 = (-∞, ∞)
We know that for every 5 red bricks there were 2 gray bricks.
The total amount of red bricks and grey bricks in this sample is 7.
5 red bricks + 2 grey bricks = 7 bricks
Now, we divide 175 "total number of bricks used" by 7 "5 red bricks + 2 grey bricks = 7 bricks" and we will get a quotient of 25.
Now we know that 25 bricks is of the wall. The gray bricks are
so we can multiply 25 by 2 and we will get a product of 50. If 1/7 = 25 grey bricks so 2/7 would be the grey bricks.
175 - 50 = number of red bricks.
Therefore, there were 125 red bricks.