Problem 1 a If r 3 inches what is the volume of the sphere I

Problem #1

a) If r= 3 inches, what is the volume of the sphere? Include units

Problem #2

a) f(g(x))

b) g(x)-f(x)

V = f(r) = (4/3)pir^3

a) r = 3 inch

V = (4/3)pi(3)^3 = 36pi inc^2

b) To find inverse :

V = (4/3)pi*r^3

r^3 = (3V/4pi)

r = f^-(V) = (3V/4pi)^1/3

c) f^-1(100) is the radius of sphere with volume 100inch^3 = ( 3*100/4*pi)^1/3

= 2.879 inch

2) f(x) = -x^2 +3x+2 ; g(x) = 2x-1

a) f(g(x)) =-(2x-1)^2 +3(2x-1) +2

= -(4x^2 +1- 4x) +6x -3 +2

= -4x^2 +10x -5

b) g(x) - f(x) = 2x -1 - (-x^2 +3x+2)

= x^2 - x-3