Precalculus (Please Help!!??)
posted by Julie .
The formula for the area of a circle and the volume of a sphere an be though of as functions of the radii of the shapes.
(Anything you could answer would be so helpful) Thank you!!
a) Write a rule expressing the area of a circle as a function of its radius. What is the domain of this function? Sketch a graph.
b) does this function have an inverse? If so, write a rule for the inverse.
C) Explain why it makes sense that the radius of a circle should be a function of its area. In what contexts would this function be useful?
d) Does the function f(x)πx^2, where x is any real number, have an inverse? Compare your answer to that in part b. Explain any differences.
e) Now write a rule expressing the volume of a sphere as a function of its radius. What is the domain of this function? sketch a graph.
f) Does this function have an inverse function? If so, write a rule for the inverse function.
g) Explain why it makes sense that the radius of a sphere should be a function of its volume. In what contexts would this function be useful?
h) Does the function g(x)=4/3πx^3,where x is any real number, have an inverse? Compare your answer to that in part f. Explain any differences.

(h) since x^3 is always increasing, there are no two values of x that give the same y. So, x^3 has an inverse
(b) not so for x^2, since there are two values of x for each y. If you restrict the radius to positive values, though, then x^2 has an inverse. Makes sense, since a negative radius makes no physical sense.
Respond to this Question
Similar Questions

math
The earth has a radius of 6,380 km. The formula for the volume of a sphere is �� V = 4/3 ðx^3, and the formula for surface area of a sphere is A = 4ðx^2 . Find the volume and surface area of the earth and write the … 
MATH
The formula for the area of a circle and the volume of a sphere an be though of as functions of the radii of the shapes. (Anything you could answer would be so helpful) Thank you!! a) Write a rule expressing the area of a circle as … 
Applied Programming
APPLIED PROGRAMMING (APR520S) ASSIGNMENT 1 Problem Solving Tools Total Marks: 50 Marks Due: Friday 22 August 2014 Suppose we want to construct a C/C++ program that can be used to calculate the area or the volume for a range of 2D … 
Computer Science
Create a class called Shapes that has a private int field named radius and the proper get and set methods (according to our Java coding standards). Create a constructor that takes an integer as a parameter to initialize the radius. … 
Math
I really do not want to fail this project, could anyone please help me understand this and go through step by step with me? 
Math, Please check answers
I do not want to fail this, could you please help me with number 1 and 3.D, and then check my other answers? 
Math
1. Find and simplify the volumetosurfacearea ratio for each of the three possible ice cube shapes. You can use this chart. Shape S/A FormulaVolume Formula Cube  S.A=6s^2  V=s^3 SphereS.A+4 pi r^2V=4/3 pi r^3 Cylinder S.A=2 … 
Math
I am doing a project, are my answers correct? 
test corrections for problems 6,11,12 and 23please
A sports team is building a new stadium on a lot of land. The lot measures 8x by 12x and the field will be 3x by 6x. how much land will be left for the bleachers, restrooms, and other parts of the stadium? 
math
1.What is the diameter of a sphere that has a volume of 3052.08 m^3?