Question

Help please ?

The function c(t)=8t+10 gives the amount c (in dollars) that you pay when you rent a kayak flr $10 and use it for time t (in hours). Write AND Interpret that inverse of this function

Answer 1

`t(c)=(t-10)/(8)` determines the time you used the kayak for at a specific cost you paid.

Explanation:

The inverse of a function, is the function or rule formed by reflecting the line over y=x. This means essentially that all (x,y) values from the original function switch to (y,x).

(x,y)--->(y,x) in the new function.

If the function has points (-3,4) and (5,-2) then the inverse has points (4,-3) and (-2, 5).

For the original function, we used the time we had the kayak to compute the cost. For 3 hours, it cost c(3)=8(3)+10=$34. (3,34) for (t,c).

For the inverse, we will find the time we had the kayak for a specific cost. To write it we switch input(x) and output(y) and solve for y.

y=8x+10

x=8y+10

x-10=8y

`(x-10)/(8) =y`

This is the inverse function, We replace (x,y) with (c,t).

`t(c)=(t-10)/(8)`