(answer)
for f(x) = 4x + 3 and g(x) = 9x find the following composite functions and state the domain of each
(a) f o g (b) g o f (c) f o f (d) g o g
(a) (f o g)(x) =

  a) 36x + 3

                b) 36x + 27

                c) 16x + 15

                d) 81x

Step-by-step explanation:

f(x) = 4x + 3         g(x) = 9x

a) f(g(x)) = 4(9x) + 3       replaced x in f(x) equation with 9x

             = 36x + 3

b) g(f(x)) = 9(4x + 3)      replaced x in g(x) with 4x + 3

             = 36x + 27

c) f(f(x)) = 4(4x + 3) + 3     replaced x in f(x) with 4x + 3

           = 16x + 12   + 3

           = 16x + 15

d) g(g(x)) = 9(9x)            replaced x in g(x) with 9x

              = 81x

solution given:

f(x) = 4x + 3

g(x) = 9x

a.fog(x)=f(9x)=4×9x+3=36x+3

domain=real number

b.gof (x)=g(4x+3)=9(4x+3)=36x+26

domain=real number

c.fof(x)=f(4x+3)=4(4x+3)+3=16x+12+3

=16x+15

domain: real number

d.

gog(x)=g(9x)=9×9x=81x

domain: real number.

then, the surface area of the sphere shown in the image is: 256π sq. units!

step-by-step explanation:

the lateral surface area of a sphere is 2πrh where h=2r.

then:

surface area = 4πr^2.

in this case, r=8 units ⇒ surface area = 4π(8 units)^2. = 256π sq. units!

then, the surface area of the sphere shown in the image is: 256π sq. units!