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

1. The area, in square centimeters, of a circle whose radius is r cm is given by A=r2.

a. Evaluate and interpret f(r)+1.

b. What are the units of f1(2)?  
Use \"cm\" for centimeters and \"cm 2\" for square centimeters. Use \"/\" to indicate a rate such as \"miles per hour\" would be written \"m/h\".

2. Find a formula for the inverse of the function

f(x)=37/x2,x>0.

f[1](Q) =

3. In the theory of relativity, the mass of a particle with speed v is m=f(v)=m01v2/c2, where m0 is the rest mass of the particle and c is the speed of light in a vacuum. Letting m0=1, find f1(10).

f1(10)=

4. Find the inverse of the following one-to-one function:

f(x)=6x+4.

(f(1))1=

Solution

1 a) f(r) = A = pi*r^2

f(r) = pi(r)^2 +1

b) f^-1(r) :

plug A = r and r =A and solve for A

r = pi*A^2

A = [ r/pi]^1/2

f^-1(r) = [ r/pi]^1/2

f^-1(2) = (2/pi)^1/2

2. f(x) = y =3 -7/x^2

Inverse : f^-1(x)

Plug x= y and y =x ans dolve for y

x = 3 -7/y^2

7/y^2 = 3-x

y = [7/(3-x)]^1/2

f^-1(x) = [7/(3-x)]^1/2

f^-1(Q) =  [7/(3-Q)]^1/2