2 points The area in square centimeters of a circle whose ra

(2 points) The area, in square centimeters, of a circle whose radius is r cm is given by A Tr2 (a) Write this formula using function notation, where fis the name of the function. Use \"pi\" for T. (b) Evaluate f(1) (c) Evaluate and interpret f(r 1). for 1) which tells us (d) Evaluate and interpret f (r) 1. f(r) 1 which tells us (e) hat are the units of f 1(5)? Use \"cm\" for centimeters and \"cm A 2\" for square centimeters. Use to indicate a rate such as \"miles per hour\" would be written \"m/h\"

Solution

A = r²

a) function f(r) = (pi) r²

b) f(r) = (pi) r²

f(1) = (pi) (1)²

==> f(1) = pi

c) f(r) = (pi) r²

f(r + 1) = (pi) (r + 1)²

==> f(r + 1) = (pi) (r² + 2r + 1) ; since (a + b)² = a² + 2ab + b²

here r is increased by 1 , i.e, (r +1) , and we got the value as (pi) (r² + 2r + 1)

Hence f(r + 1) is the area when the radius is increased by 1cm . (the units of length is cm)

d) f(r) + 1

==> f(r) + 1 = (pi) r² + 1

here 1 is added to the function f(r) , hence we got the value as (pi) r² + 1

which tells us, the area of circle with 1 sq. cm. more than a circle with radius r. (since the units for area is sq. cm.)

e) f ^-1(5)

Now, units of f(r) is sq. cm. , units of r is cm.

f(r) = (pi) r²

let f(r) = y sq.cm ==> r = f^-1(y) cm.

==> (pi) r² = y

==> r² = (y / pi)

==> r = [y / (pi)]

==> f^-1(y) = [y / (pi)] cm.

Hence units of f^-1(5) = [5 / (pi)] are cm.