SOLUTION: I have been working on this problem for about an hour. I am ready to toss it out the window! 1) Let f(x) compute the time in hours to travel x miles at 58 miles per hour. 2)Wha

Question 114569: I have been working on this problem for about an hour. I am ready to toss it out the window!
1) Let f(x) compute the time in hours to travel x miles at 58 miles per hour.
2)What does f-1(x) compute?
Thanks so much.
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
#1

If we use the equation , then solving for t we get . Since we know that we're traveling at 58 mph, this means r=58. So we then get . Now since we want to find the time based on a given distance, t will be dependent on D (whatever D is, t will be affected by it). So this means D is x (our input) and t is f(x) (our output)

So our equation is:

So if we traveled 58 miles, then we simply plug it in:

And simplify

Since f(x) is t, the time it takes to travel 58 miles going 58 mph is 1 hour.

#2

Now to find , simply switch x and f(x) to get

Now solve for f(x)

Multiply both sides by 58

So our inverse function is

Now heres what happened: When I switched x and f(x), I really switched t and D. So now the distance D is dependent on the time t (whatever t is, D will be derived from t). So for the inverse, x is now t and f(x) is now D. Basically, the inverse now computes the distance given a certain time (instead of a certain computing a certain time given a distance).

Is this making sense?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1) Let f(x) compute the time in hours to travel x miles at 58 miles per hour.
2)What does f-1(x) compute?
-----------------------
f(x) = distance/rate = x miles/58mph
--------
The domain of f(x) is "miles traveled"
The range of f(x) is "time required to travel that number of miles".
------------------------
f^-1(x) = rate*time = 58 mph*time = distance
f^-1(x) interchanges those:
The domain is time you travel
The range is miles you go in that time.
--------------------------------------
Cheers,
Stan H.
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