1. The area, in square centimeters, of a circle whose radius is r cm is given by
ID: 3412145 • Letter: 1
Question
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=
Explanation / Answer
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
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