Answer:
B.
![{ \tt{f(x) = \sqrt[3]{x + 11} }}](https://tex.z-dn.net/?f=%7B%20%5Ctt%7Bf%28x%29%20%3D%20%20%5Csqrt%5B3%5D%7Bx%20%2B%2011%7D%20%7D%7D)
let the inverse of f(x) be m:
![{ \tt{m = \sqrt[3]{x + 11} }} \\ { \tt{ {m}^{3} = x + 11}} \\ { \tt{ {m}^{3} - 11 = x}} \\ { \tt{ {f}^{ - 1}(x) = {m}^{3} - 11 }}](https://tex.z-dn.net/?f=%7B%20%5Ctt%7Bm%20%3D%20%20%5Csqrt%5B3%5D%7Bx%20%2B%2011%7D%20%7D%7D%20%5C%5C%20%7B%20%5Ctt%7B%20%7Bm%7D%5E%7B3%7D%20%20%3D%20x%20%2B%2011%7D%7D%20%5C%5C%20%7B%20%5Ctt%7B%20%7Bm%7D%5E%7B3%7D%20%20-%2011%20%3D%20x%7D%7D%20%5C%5C%20%7B%20%5Ctt%7B%20%7Bf%7D%5E%7B%20-%201%7D%28x%29%20%3D%20%20%7Bm%7D%5E%7B3%7D%20%20-%2011%20%7D%7D)
substitute for x in place of m:
![{ \bf{f {}^{ - 1}(x) = {x}^{3} - 11 }}](https://tex.z-dn.net/?f=%7B%20%5Cbf%7Bf%20%7B%7D%5E%7B%20-%201%7D%28x%29%20%3D%20%20%7Bx%7D%5E%7B3%7D%20-%2011%20%20%7D%7D)
First of all, observe that the graphed function is
.
Now, if we want to shift the graph 4 units up, it means that we want each point on the graph enlarge its y coordinate by 4: we no longer want to associate
![x\mapsto y](https://tex.z-dn.net/?f=x%5Cmapsto%20y)
but
![x\mapsto y+4](https://tex.z-dn.net/?f=x%5Cmapsto%20y%2B4)
And since
, we want to map
![x\mapsto f(x)+4](https://tex.z-dn.net/?f=x%5Cmapsto%20f%28x%29%2B4)
And in our case,
, so the answer is
![\sin(x)+4](https://tex.z-dn.net/?f=%5Csin%28x%29%2B4)
To convert from kilometers into miles, multiply the distance in kilometers by 0.6214.
13 yards because there is 3 feet per yard so I divided 40 by 3 and I got 13.3333...... So I rounded that to 13. Hope that helped! :)
I got you, the answer would be x=5