The complete question in the attached figure
we know that
area of semi circle=pi*r²/2
diameter=5 ft
radius r=5/2----> 2.5 ft
so
area of semicircle=pi*2.5²/2-----> 9.8125 ft²
<span>the area of each stained glass section=area semicircle/3
</span><span>the area of each stained glass section=9.8125/3----> 3.27 ft</span>²---> 3 ft²
the answer is3 ft²
<em><u>Solution:</u></em>
Given that:
To find: (fog)(2) and (f + g)(2)
By composite function,
( f o g)(x) = f (g(x))
Substitute g(x) = 4x + 9 in above formula,
( f o g)(x) = f(4x + 9)
To find (fog)(2) substitute x = 2 in above formula
( f o g)(2) = f(4(2) + 9)
( f o g)(2) = f(8 + 9) = f(17)
We know that
<em><u>To find (f + g)(2)</u></em>
We know that,
(f + g)(x) = f (x) + g(x)
Therefore,
(f + g)(2) = f(2) + g(2)
Substitute x = 2 in f(x) and g(x)
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