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# Domains + Ranges of functions watch

1. What does x e R mean? In my book it says: X is a member of the set of real numbers. What are real numbers?

Can anyone tell what the range of these functions are, with domain x e R:

a) f(x) = x²-1

b) g(x) = (x-1)²

c) h(x) = x³ + 3x

Thank you....sorry if they seem like simple questions.
2. (Original post by Mushu)
What does x e R mean? In my book it says: X is a member of the set of real numbers. What are real numbers?

Can anyone tell what the range of these functions are, with domain x e R:

a) f(x) = x²-1

b) g(x) = (x-1)²

c) h(x) = x³ + 3x

Thank you....sorry if they seem like simple questions.
im not sure about the proper definition but real numbers are all numbers that you can think of, negative and positive, rational or irrational.

1) range is f(x) is all real numbers greater than or equal to -1 (i cant find the sign)

2) range is f(x) is all real numbers greater than or equal to 0

3) range is all real numbers
3. A real number is just any rational or irrational number (that exists, it doesnt include complex numbers)
4. (Original post by Undry1)
im not sure about the proper definition but real numbers are all numbers that you can think of, negative and positive, rational or irrational.

1) range is f(x) is all real numbers greater than or equal to -1 (i cant find the sign)

2) range is f(x) is all real numbers greater than or equal to 0

3) range is all real numbers

Thanks for that. I don't understand how you get the range, i know its the y values but can u just tell me how u got them
5. for:

a) you just look what the minimum value is. Anything that is squared becomes positive, so the minimum value of x^2 is 0. when x = 0, the value of y is -1, therefore the range is any number greater than -1.

b)Again, if calculation inside the brackets is negative, it will become positive, so the minimum value is when the calculation of the brackets is zero, i.e x-1 = 0, when x is eual to 1
6. (Original post by Mushu)
Thanks for that. I don't understand how you get the range, i know its the y values but can u just tell me how u got them
for quadratics, its best to have it in completed square form, then you can see the minimum or maximum point.
eg, for the first one x²-1,
x² has the minimum y value of 0. x²-1 is just translated (moved) 1 unit down.
so the minum y value becomes -1. there is no maximum value so y can take any value above or equal to -1
7. (Original post by Mushu)
Thanks for that. I don't understand how you get the range, i know its the y values but can u just tell me how u got them
I find it easiest to sketch the graphs of the functions in your head.

If necessary use calculus to find max/min points to give an answer.

You may also want to see http://www.thestudentroom.co.uk/t120438.html where I (and others) answer this question more fully.
8. General method: To differentiate function, and find turning points and find the minimum/ maximum point of the function. Then deduce the range.

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