Find the domain of the function

In summary, the conversation is about finding the domain of a function, specifically f: x mapsto 1/sqrt(x^2 - 10x + 12). The definition of domain is discussed and the person is asked to show their attempts at finding the domain. After realizing there was an error in the original function, it is corrected to f: x mapsto 1/sqrt(x^2 - 10x + 21). The person then factors the expression and determines that the domain is [3; 7].
  • #1
kebstein
4
0
hi this is my first time here. i have just been admitted to the university of the gambia last month. i have a problem with this question. please i need help

find the domain
f is such that x maps to 1 all over the squareroot of x2-10x+12.
 
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  • #2


I assume you meant
[tex]f: x \mapsto \frac{1}{\sqrt{x^2 - 10x + 12}}[/tex].

What is the definition of domain? How would you go about finding it?
 
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  • #3


yeah this is what i meant,
 
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  • #4


OK, so can you show us some attempt / ideas you had (no matter how stupid you think they are)? You completely ignored the template that pops up when posting a question, but it's there for a good reason. We are not too good at guessing what you do and don't know; moreover the idea is we just help you find the answer yourself, instead of just giving it to you.
 
  • #5


you were asked before, what is the definition of "domain". If you know that definition, please tell us what it is. If you don't, look it up! You can't hope to do problems involving words you don't know!
 
  • #6


there is an error in my first question. it should
f: x mapsto frac{1}{\\sqrt{x^2 - 10x + 21}')
 
  • #7


i think i have to factorize x2-10+21
x2-3x-7x+21
x(x-3)-7(x-3)
(x-3) (x-7)

x-3 is greater than or equal to 0 and x-7 is greater than or equal 0
there for x is greater than or equal to 3 and x is greater than or equal to7

then Df = [3; 7]

is this correct
 
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1. What is the definition of a domain?

The domain of a function is the set of all possible values for the independent variable. In other words, it is the input values that the function can accept.

2. How do you find the domain of a function algebraically?

To find the domain of a function algebraically, you need to look for any restrictions on the independent variable. These can include division by zero, taking the square root of a negative number, or logarithms of non-positive numbers. You also need to consider any restrictions given in the problem or by the context of the function.

3. Can the domain of a function be a negative number?

Yes, the domain of a function can include negative numbers. The domain can include any real number that is not restricted by the function or the context of the problem.

4. What does it mean if a function has no domain?

If a function has no domain, it means that there are no values that the independent variable can take to produce a valid output. This could happen if the function is undefined for all values of the independent variable or if the function has a vertical asymptote that the independent variable cannot cross.

5. How does the domain of a function relate to its graph?

The domain of a function is represented on the x-axis of the graph. The points on the graph that fall directly above or below the domain values are the corresponding outputs of the function. Any points on the graph that do not align with a domain value are not part of the function.

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