What is the policy about blank assignments?
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Answer:
The number of ways are there to paint the four buildings is 48.
Step-by-step explanation:
I) let the first building be any color. Therefore the first building can be painted with any of the 4 colors.
Therefore the first building can be colored in 4 ways.
ii) the second building can be colored in 3 ways since it cannot be colored the
same color as the first building.
iii) the third building can also be colored in 3 ways.
iv) the last building can be colored in 2 ways because it cannot be the same color as the first building or the color of the adjacent building.
Therefore the total number of ways the buildings can be colored = 4 3
3
2 = 48.
Answer:
The function h (x) = StartFraction 11 Over x minus 4 EndFraction
has the domain of h (x) = ( - ∞, 4) U (4, ∞ ) which is same as the
domain of (m ∘ n)(x) = ( - ∞, 4) U (4, ∞ ).
Step-by-step explanation:
m (x) = StartFraction x + 5 Over x minus 1 and n(x) = x – 3
As m (x) could be written as:
n(x) = x – 3
(m ∘ n)(x) = m(n(x)) = m(x – 3)
=
=
In order to find the domain of (m ∘ n)(x) = , we need to
make sure that denominator can not be zero,
So,
x - 4 = 0
x = 4
So, our domain can be anything except for 4.
Hence, Domain = D = ( - ∞, 4) U (4, ∞ )
Now, compare the domain of (m ∘ n)(x) i.e D = ( - ∞, 4) U (4, ∞ ) with all the options:
Option A: h (x) = x + 5 / 11
Option A has the Domain of h (x) = Set of all real numbers
So, Option A is false.
Option B: h (x) = 11 / x - 1
x - 1 = 0
x = 1
Option B has the domain of h (x) = ( - ∞, 1) U (1, ∞ )
So, Option B is false.
Option C: h (x) = 11 / x - 4
x - 4 = 0
x = 4
Domain C has the domain of h (x) = ( - ∞, 4) U (4, ∞ )
So, Option C is true.
Option D: h (x) = 11 / x - 3
x - 3 = 0
x = 3
Option D has the domain of h (x) = ( - ∞, 3) U (3, ∞ )
So, option D is also false.
Hence, only option C is true as the option C i.e. h (x) = StartFraction 11 Over x minus 4 EndFraction has the domain of h (x) = ( - ∞, 4) U (4, ∞ ) which is same as the domain of (m ∘ n)(x) = ( - ∞, 4) U (4, ∞ ).
keywords: Domain, composite function
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