How to determine maximum domain from function statements

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mimie

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I would like someone to help me with 2(b) and 2(d) of the question. I also do not know how to make them in inverse form.12229
 
Hello, and welcome to FMH! :)

(b) We are given a quadratic function. Can you determine the axis of symmetry?
 
Can I correctly assume that you have solved 2(a)? It will be helpful to see what you did there, so we can extend it to (b).

Note that you are not asked to actually find the inverse function; that can be done for all except (d), I think, but you don't have to.

On the other hand, it will be very helpful to you if you at least sketch the graph of each function to see why they are not one-to-one, and how restricting the domain would help.

But there's a problem: unless you were given some special definition of "maximum domain", none of the problems has a unique answer. Do you have an example of the sort of answer they expect (from an example or an answer in the back)?
 
They are not asking you to find the inverse. They are merely asking you to find a domain of the specified function such that it can have an inverse. You can think of this as first finding where the function cannot have an inverse.
 
MarkFL said:
Hello, and welcome to FMH! :)

(b) We are given a quadratic function. Can you determine the axis of symmetry?
Click to expand...

for 2(b), I was able to find minimum point for the graph and sketch it, but the answer at the back of the book is x ∈ A , x ⩽ 2.
I dont understand how and why? Please explain to me, thanks.
12230
 
Yes, \(x=2\) is the axis of symmetry, so I would give as my answer that the equally sized domains are where the function is one-to-one:

[MATH](-\infty,2][/MATH]
[MATH][2,\infty)[/MATH]
I don't see why they would favor the right half over the left half. :)
 
MarkFL said:
Yes, \(x=2\) is the axis of symmetry, so I would give as my answer that the equally sized domains are where the function is one-to-one:

[MATH](-\infty,2][/MATH]
[MATH][2,\infty)[/MATH]
I don't see why they would favor the right half over the left half. :)
Click to expand...

How about 2(d)?
 
mimie said:
How about 2(d)?
Click to expand...

Unless you are familiar with techniques in differential calculus for determining the turning points (since you posted in the Pre-Algebra forum I am assuming you have not studied the calculus yet), you'll have to rely on a graph of the function:

fmh_0053.png

I have labeled the turning points, and shaded the 3 domains on which the function is one-to-one. They are:

[MATH]\left(-\infty,-\frac{2}{3}\right][/MATH]
[MATH]\left[-\frac{2}{3},0\right][/MATH]
[MATH][0,\infty)[/MATH]
 
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