The area in square centimeters of a circle whose radius is r

The area, in square centimeters, of a circle whose radius is r cm is given by A = pi r^2. (a) Write this formula using function notation, where f is the name of the function. f(r) = (b) Evaluate f(0) = (c) Evaluate and simplify the formula for f (r + 1) = (d) Evaluate and simplify the formula for f (r) + 1 = (e) Evaluate, including units in your answer:f^-1 (4) =

Solution

a. f(r)= pi r²

b. f(0)=pi * 0²=0

c. f(r+1)=pi (r+1)² = pi(r²+2r+1)= pi r²+ 2 pi r + pi

d. f(r) + 1= pi r²+1

e. f^-14

f(r)= pi r²

A= pi r²

First we have to switch A and r

r=pi A²

A=sqrt(r/pi)

f^-14 = sqrt(4/pi)=2/sqrtpi