I am having trouble with the following question.

Two functions are defined as

a) Find the smallest possible value of a given that the domain of the function h, where , is a is less than or equal to x and 2 is greater than or equal to x

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- February 22nd 2011, 04:08 AMjohnsy123Sum, product and difference of function question
I am having trouble with the following question.

Two functions are defined as

a) Find the smallest possible value of a given that the domain of the function h, where , is a is less than or equal to x and 2 is greater than or equal to x - February 22nd 2011, 04:50 AMSambit
- February 22nd 2011, 06:25 AMHallsofIvy
I presume that you mean you want to find a so that is the domain of .

Okay, what kinds of numbers would NOT give a value for ?

(Hint: you can ignore the term.) - February 22nd 2011, 06:47 AMSoroban
Hello, johnsy123!

Very clumsy and misleading wording!

WHO wrote this question?

. . Public flogging may be appropriate punishment.

Quote:

. . . .

Now that I understand the problem, it's*too easy.*

We have: .

We see that must be nonnegative.

So, the domain is: .

. . Therefore: . . .*Duh!*

- February 22nd 2011, 12:22 PMjohnsy123
How does a=0? why can't a= 1 or a=2?

All negative numbers.

And i have one more question, if thats okay.

How would i find the range of that function? - February 23rd 2011, 04:48 AMHallsofIvy
Because they are not

**smallest**. And your problem asked you to "Find the smallest possible value of a".

??? What is this in response to? There are no negative numbers in the domain of square root if that is what you meant.

Your function is with . It is easy to see that the smallest value of f(x) occurs when x= 2: but the maximum value is harder. I recommend graphing the function between x= 0 and x= 2.