Precalculus (Please Help!!??)
posted by Julie on .
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.