Answer:
4989600
Step-by-step explanation:
The given word is MATHEMATICS
Number of letters in the given word is 11
there are 2 M's, 2 A's and 2 T's
the given word is arranged in 11! ways
three letters are repeating, so we divide by repeating occurrences
number of different arrangements =
= 4989600
and h(x)= 2x-8
g o h is a composition function
First we find g o h
g o h is g(h(x))
We plug in h(x) in g(x)
We replace x with 2x-8 in g(x)
To find domain we look at the domain of h(x) first
Domain of h(x) is set of all real numbers
now we look at the domain of g(h(x))
Negative number inside the square root is imaginary. so we ignore negative number inside the square root
So to find domain we set 2x - 12 >=0 and solve for x
2x - 12 >=0
add both sides by 12
2x >= 12
divide both sides by 2
x > = 6
