Question

Suppose f , g , h , and j are functions such that: f ( r ) represents the circumference (in cm) of a circle whose radius is r cm. g ( C ) represents the radius (in cm) of a circle whose circumference is C cm. h ( r ) represents the area (in cm2) of a circle whose radius is r cm. j ( A ) represents the radius (in cm) of a circle whose area is A cm2.

a. Use function notation to represent the area of a circle whose circumference is 133 cm.
b. Use function notation to represent the circumference of a circle whose area is 6.82 cm^2

Answer 1

(a)h(g(133))

(b)f(j(6.82))

Explanation:

(a)Area of a circle whose circumference is 133 cm.

Since g(C) represents the radius (in cm) of a circle whose circumference is C cm.

• The radius of the circle whose circumference is 133 cm = g(133)

h(r) represents the area
`(in$ cm^2)` of a circle whose radius is r cm.

• Area, h(r) =h(g(133))

Therefore, the area of a circle whose circumference is 133 cm is:

h(g(133))

(b)Circumference of a circle whose area is
`6.82 cm^2`

j(A) represents the radius (in cm) of a circle whose area is A
`cm^2`.

• The radius of the circle of area
  `6.82 cm^2` = j(6.82)

f(r) represents the circumference (in cm) of a circle whose radius is r cm.

Therefore:

• Circumference, f(r) = f(j(6.82))

The circumference of a circle whose area is
`6.82 cm^2` =f(j(6.82))