Domain of the Function f(x): Explained

In summary, the domain of the function f(x)= log_{5}(log_{5}(x + 2)) is (-1, \infty). This is because in order to take the log of x+2, both x+2 and log_{5}(x+2) must be greater than or equal to 0. This means that x+2 must be greater than or equal to 1, giving the domain of (-1, \infty). Additionally, the log_{5}(x+2) cannot equal 0, so x+2 cannot equal 1, resulting in the exclusion of -1 from the domain.
  • #1
the_storm
42
0
The Question is: What is the Domain of the function f(x)= log[tex]_{5}[/tex](log[tex]_{5}[/tex](x + 2)
My answer is that the Domain is (-2, [tex]\infty[/tex]). However the it is said that the right answer is (-1, [tex]\infty[/tex]) and I am not convinced so can anyone give me an explanation?
 
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  • #2
You can't take logs of negative numbers. So you'll need to make sure that

[tex] x+2\geq 0 [/tex]

But there's another log in that formula. That log also can't take negatives as input. So moreover, you'll have to make sure that

[tex]\log^5(x+2)\geq 0 [/tex]
 
  • #3
so Domain is (-1, infinty) right??
 
  • #5
Just nitpicking to pass the morning. It's not just negative numbers you can't take the log of. It's also zero. You can't take the log of a non-positive number. No?
 
  • #6
You cannot take the log of zero.
 
  • #7
If we are nitpicking: "the domain" of a function is part of the definition of that function. OP is asking for the largest possible domain that is compatible with the given formula.
 
  • #8
It's true Landau, but nobody disputed that.
 
  • #9
can you be more explicit
 

1. What is the domain of a function?

The domain of a function is the set of all possible input values for the independent variable (usually denoted as x) that will produce a valid output from the function. In other words, it is the set of values for which the function is defined.

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

To find the domain of a function, look for any values of the independent variable (x) that would result in an undefined output. These could include dividing by zero, taking the square root of a negative number, or any other operations that are not defined for certain values. Other than these restrictions, the domain is typically all real numbers unless specified otherwise.

3. Can the domain of a function be negative?

Yes, the domain of a function can include negative numbers as long as they do not result in an undefined output. For example, a function with a square root cannot have a negative input, but a function with a logarithm can have a negative input as long as it is not zero.

4. How can the domain of a function affect its graph?

The domain of a function can affect its graph by limiting the range of values that can be plotted on the x-axis. If the domain is restricted to only positive numbers, for example, the graph will only show points on the positive side of the x-axis. It can also affect the shape of the graph, as certain restrictions on the domain may result in discontinuities or breaks in the graph.

5. Can a function have an infinite domain?

Yes, a function can have an infinite domain if there are no restrictions on the values of the independent variable. This means that the function is defined for all real numbers, and there is no upper or lower bound on the domain. For example, the function y = x can be defined for all real numbers, making its domain infinite.

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