Question

The police can determine the speed a car was traveling from the length of the skid marks it leaves. The function they use is S = f(L) = 2sqrt(5L) where S is speed (mph) and L is the length of the skid marks (feet)

(a) If skid marks of length 125 feed are measured, what was the speed of the car

Inputting 125 in the formula i get 50 mph

(b) find the formula for the inverse function.

f^-1(S) = ?

How would i find the inverse?

Answer 1

a) is correct

b) since the S and L are defined variables, taken the inverse in the usual way changes their definitions.
We could just follow the usual steps ...
if S = 2√(5L) , the inverse is obtained by interchanging the variables, so
inverse is
L = 2√(5S)
we would then solve this new equation for S
L^2 = 4(5S)
L^2 = 20 S
S = L^2/20 , which is totally meaningless and false for our defined values of S and L, as speed and length of skid mark.

I think b) is poorly stated and they probably meant to solve for L in terms of S
which would be:
S = 2√(5L)
S^2 = 4(5L) = 20L
L = S^2/20
notice if we plug in 50 for the S as speed
we get L = 50^2/20 = 125, which was out initial input

Answer 2

82.697