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# P2 range and domain! watch

1. I get kinda confused with these questions...here's one for instance:

P2 Jan 2003

8(c) (ii) find the range of f(x) when:

f(x) = 3(2^-x) - 1, x is a real number, x >= 0

Also can someone just give a general method of finding the range/domain of a function? I can find the range for a quadratic function...but for some others (like the above) i struggle...

thx
2. ok

x=0

f(x) = -1

put any number bigger than x

you should see that f(x) > 1

therefore the range is f(x) >= 1
3. for the inverse of the function...

the domain of the function would be the range of the inverse

the range of the function would be the domain of the inverse

for instant, take

f(x) = x2 and f-1(x) = x1/2

For f(x) = x2

the domain of the function is,

x is any real number

range,

f(x) > or = 0

For f-1(x) = x1/2

domain of the function

x > or = 0

range,

f-1(x) is any real number

also, another good thing about inverse graphs is that they are reflections in the line y=x

good luck if you have p2 tomorrow like me!!!
4. (Original post by Revenged)
ok

x=0

f(x) = -1

put any number bigger than x

you should see that f(x) > 1

therefore the range is f(x) >= 1
This range and domain stuff confuses the hell out of me also, got c3 in the morning aswell!!!!!!!!!!!!!! i know that the range for an inverse function is its domain, but this doesnt seem to work for all questions. AM I GOING MAD??? Someone please help
5. thx revenged....i get what u r saying but there are still some questions where i get confused with the range/domain...
6. well... sometimes you need to differenciate to find the minimum value of x and then find f(x) but that's as hard as it gets

also the modulus signs are a problem but i don't know what you need to do for c3... i got p2 tomoz
7. ok so basically just find the lowest value possible for x and then slam it into the equation???
8. well... for y = ax^2 it's the minimum as the graph is 'u shape'

for y = -ax^2 it will be the maximum as the graph is 'n shape'
9. alright cool. some of them are x bigger than __ smaller than __
are these x^3 functions?
The thing that confuses me is that these are only usually 2-3 mark questions, and they are LONG
10. Oh yeah I know them questions, I just posted a thread with a question asking for the range of x(x-6) and i was lyk... ?????, but I actually forgot I had to differentiate it!!! DUH!!
11. for quadratics its easy to find range
first differentiate the function
make the derivative = 0 as thats when min/max (stationary/turning) points occur
find the value of x for which derivative = 0
put that back into orignal quadratic and find the min/max value
to find out whether it is a min or a max just find the second derivative and if second derivative>0 then min, if less than 0 then max
12. ****!!! i understand, i see the light!!!!! thanks Devesh. So is it actually easier for quadratics??
13. much easier for quadratics....infact that method i gave should work for all polynomials...when it says range it basically asks for the minimum/maximum (i.e. stationary points)...but i get confused with ones which you cant differentiate...!
14. I actually like it the other way!!

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