The function notation f(x)=2x-4 means replace the x on the right-hand side with the value in parentheses on the left.
For example, f(y)=2y-4; f(4)=2(4)-4=4; f(1)=2(1)-4=-2 and so on.
The same principle applies to g(x), for example
g(2)=4(2^2)-3=13,
g(x+1)=4(x+1)^2-3=4(x^2+2x+1)-3=4x^2+8x+4-3=4x^2+8x+1
and so on.
(g of f)(x) is another way to write g(f(x)), therefore
g(f(x))
=g(2x-4) [because f(x)=2x-4
=4(2x-4)^2-3
=4(4x^2-16x+16)-3
=16x^2-64x+64-3
=16x^2-64x+61
g(x) = 2x-6
f(x) = -4x +7
(g•f)(x) = g(f(x))
= 2(f(x)) - 6
= 2 ( -4x+7) -6
= -8x + 14 -6
= -8x +8
now
(g•f)(1) = -8(1) + 8= -8+8
= 0
so option a is answer
Answer:
The circle is centered at (-8,3) and has a diameter of 20 units
Step-by-step explanation:
we know that
The equation of a circle in center radius form is equal to

where
(h,k) is the center of the circle
r is the radius of the circle
In this problem we have

so
The center is the point (-8,3)
The radius is 
so
The diameter is two times the radius

therefore
The circle is centered at (-8,3) and has a diameter of 20 units
You want to find the volume inside the hemisphere
(i.e. inside the sphere but above the plane
) and outside the cylinder
. Call this region
.
In cylindrical coordinates, we have



(where
)

