Maths questions...SAVE ME NOW!

[sno]

1. Functions f and g are defined on the domain of all real numbers as follows:

f(x)=[x]
g(x)=x-[x]

A (i) Find the range of f and g
(ii) Find fg(x)

2. limit (x tending to 0) [(4+5 power 1/x) / (3+5 power 1/x)

3. [|x| / x2-1] > 0

[Zeroth]

i think range of f(x) is infinity while g(x) is infinity as well. Not sure about g(x) though.. my maths karat liau..

[aim]

Err...sno, sorry la. My lecturer started off with statistics and geometry, so I won't be able to solve such questions yet.

Don't be so stressed out lar...lay back then think about it again.

[khor_albert]

Originally Posted by aim

Err...sno, sorry la. My lecturer started off with statistics and geometry, so I won't be able to solve such questions yet.

Don't be so stressed out lar...lay back then think about it again.

Sorry, it was me. I was using aim's computer and doesn't realise that I am using his profile. Sorry for the inconveniences.

[sabishii]

for the first part,
f(x) has a range of {X|X is an integer}
similiarly, from the properties of the [x], (assuming that [x] is referring to a step function, that is.)

g(x) will have a range of [0,1)

the second question seemed to be a typical example of using the L'Hospitals rule. Since the L'Hospital condition is satisfied, differentiating both top and bottom giving you '1' after doing all those.

another way is to simply break the 4+5^(1/x) apart, and make it 1+ {3+5^(1/x)} the latter part gets cancelled off and you're left with an equation where you could simply plug in the numbers. you'll still get 1

didn't get the third question, sorry

[petertok]

Originally Posted by sno

1. Functions f and g are defined on the domain of all real numbers as follows:

f(x)=[x]
g(x)=x-[x]

A (i) Find the range of f and g
(ii) Find fg(x)

2. limit (x tending to 0) [(4+5 power 1/x) / (3+5 power 1/x)

3. [|x| / x2-1] > 0

what innovative way to get ur maths questions done, sno.

[sabishii]

Originally Posted by petertok

what innovative way to get ur maths questions done, sno.

haha, i guess he was simply desperate to get it done.

[joebf86]

what is L'Hospital rule?

[khor_albert]

Originally Posted by sabishii

haha, i guess he was simply desperate to get it done.

Hahaha.....sno's a SHE...just trying to clarify here.

However, good solution being made. I learned something.

[byzhanii_bogn]

Originally Posted by joebf86

what is L'Hospital rule?

what has this to do with that? our lecturer started with the easier ones, number system, polynomial, sequences... u know...

but the questions are on functions right?