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# Stuck on range of a function watch

1. The functions f and g are defined by

f(x) = x2 – 3x + 7

g(x) = 2x – 1

Find the range of f

I hasten to add this isn't my question it's a mate's who I'm revising with. Any help would be much appreciated!
2. The range of f(x) for when it is less than? greater than or equal to g(x) ??
3. Sorry wasn't told to add that bit as well!

Apparantly, "f(x) must be positive". This is the only bit of the question he's stuck on and it's the first bit.....
4. (Original post by corkskrew)
The functions f and g are defined by

f(x) = x2 – 3x + 7

g(x) = 2x – 1

Find the range of f

I hasten to add this isn't my question it's a mate's who I'm revising with. Any help would be much appreciated!
Its best to differentiate the function to find the minimum point, all values above this point will be the range of the function.
for f(x) the range is x » 4.75
so greater than or equal to 4.75.

f(x) is always positive, because the function has x², which will turn all negative x values into positive.
5. (Original post by Vijay1)
The range is x » 5
so greater than or equal to 5.

f(x) is always positive, because the function has x², which will turn all negative x values into positive.
I always thought that when you had a quadratic you had to complete the square to find the range, is this right????
6. (Original post by fabz)
I always thought that when you had a quadratic you had to complete the square to find the range, is this right????
Ah, by completing the square, that is to find the solution of the equation (e.g the value of x for which the function = 0)

The range is by differentiation or else another method.
7. (Original post by Vijay1)
Ah, by completing the square, that is to find the solution of the equation (e.g the value of x for which the function = 0)

The range is by differentiation or else another method.
yeah but, no but...

If you complete the square you get (x- (3/2))²+4.75, so the value of f(x) has to be greater than 4.75!!!
8. (Original post by fabz)
yeah but, no but...

If you complete the square you get (x- (3/2))²+4.75, so the value of f(x) has to be greater than 4.75!!!
Oh, I see, well thats another method.
I prefer my method.

But we are essentially doing the same thing! that is finding the vertex (the lowest point on the graph of the function)
9. So if you differentiate any function do you get the range or does it only apply to some?
10. (Original post by fabz)
So if you differentiate any function do you get the range or does it only apply to some?
No, what happens is by completing the square on a quadratic your finding the vertex of the function hence the minimum point. So completing the square can be done for finding range for quadratic function.

But just think a cubic function can have 2 turing points, by differentiating you find both points (which can't be done with other methods such as completing the square because it only works with quadratics) so differentiating to find turning points and the minimum point allows to deduce the range.

Obviously, differentiating is the general method to find range for all functions.
11. Thanks, that has been bothering me for ages! If I get an A on thursday you can take some credit!!
12. (Original post by fabz)
Thanks, that has been bothering me for ages! If I get an A on thursday you can take some credit!!
Good luck
13. Thanks for the help all :-)
14. what exam board u doin? i have no maths exams on thurs? lol stop scaring me like that!
15. (Original post by ZooBOT)
what exam board u doin? i have no maths exams on thurs? lol stop scaring me like that!
I've got (normal) OCR M1 and C3

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