Question

And the question below

Answer 1

(a) 2nd Choice: The amount of time he has walked (in hours) when he is x kilometers from Glen City

(b)
`D^(-1)(x) = (11.6 - x )/(4)`

(c)
`D^(-1)(6.4) = 1.3 \;\text{hours}`

Explanation:

(a)

Since D is distance in km from Glen City after t hours of walking, the inverse D⁻¹ would be the time taken in hours to walk x kilometers from the city. So the second choice

(b)

`D^(-1)(x) = (11.6 - x )/(4)`

To find the inverse of a function y = f(x), interchange y and x and solve

y = 11.6 - 4x (using x instead of t)
Interchange y and x ==> x = 11.6 - 4y

Add 4y to both sides ==> 4y + x = 11.6 - 4y + 4y = 11.6

Subtract x from both sides ==> 4y = 11.6 - x

Divide both sides by 4 ==> y = (11.6 - x)/4

(c)
`D^(-1)(6.4) = (11.6 - 6.4 )/(4) = (5.2)/(4) = 1.3 \;\text{hours}`