Does this make sense mathematically?

For question 2, I don't see a right answer either, but in 5, they want the limit as x approaches infinity, which I believe is e to the power of R.

I contend that he answer to question is simply 'e' not 'e to the r power'.

For question 2:

The answer is D because:

So:
f(y) < (4-y) / 3 (y now becoming the independant variable)
OR since there is only one variable, renamed to x:
f(x) < (4-x) / 3

Since I've never been taught math in English, I do not know the expression 'compounding' and I am too lazy to look it up

Chucara
Chucara,
Pardon my ignorance, but all makes sense to me until you say:

"OR since there is only one variable, renamed to x:
f(x) < (4-x) / 3." How can this be assumed.

The initial inequality implies that f(x) is another function of x different from (4-3x). Suppose that initially f(x)=4-4x. This particular f(x) is less that 4-3x for all x>0.

But it does not satify the condition that 1/f(x) < (4-x)/3 for x>4. Let x =10; then -36<-26. OK. Then nonsense results. 1/f(x)=-1/36 and (4-x)/3= -2 and -1/36 is not less than -2.

Where did I miss it? Are there some assumed initial conditions that were not stated?

Well.. this is a bit diffucult for me to explain in english, but here goes:

Seeing as we've used the <=> symbol allthrough the inequation, the final line corrosponds the same function as the first line. In order to find the inverse function f^(-1)(x), we have to switch places of x and y.

By definition, the inverse function is the function that'll let you go from a value of y to a value of x - instead of a value of x to a value of y.

In other words, f-1(x) is f(x) mirrored by the axis y = x - as shown below:


Hope that explains it.. otherwise I'll be back to try to answer more questions

Thanks Chucara, for the info and the graph. I appreciate your going to the trouble. What you presented has explained the problem for me. TripleM

Brandon9000
In question you say they are asking for the limit as x approaches infinity. Am I looking at the wrong question paper as I see no possibility of this, x is not even a variable. The answer was simple I thought, 5.00pm, as it takes 4 hours to reach its max. displacement.
Please can someone clarify this as I am very confused.

They appear to have changed the questions.

That would probably explain it!