What is the domain of $x^{2x}$
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What is the domain of $f(x)=x^{2x}$?
If $f(x)=(x^2)^x $then $f$ is defined for every real number but if $f(x)=(x^x)^2$ then $f$ is only defined and "nice" (excluding the negative $-p/q$ fractions) for positive real numbers.
Should we say $f(x)=e^{2xlog(x)}$ is only defined for positive $x$?
Thanks
calculus functions
asked Nov 17 at 12:51
Pedro
510212
add a comment |
up vote
2
down vote
favorite
What is the domain of $f(x)=x^{2x}$?
If $f(x)=(x^2)^x $then $f$ is defined for every real number but if $f(x)=(x^x)^2$ then $f$ is only defined and "nice" (excluding the negative $-p/q$ fractions) for positive real numbers.
Should we say $f(x)=e^{2xlog(x)}$ is only defined for positive $x$?
Thanks
calculus functions
asked Nov 17 at 12:51
Pedro
510212
For $f(x)=(x^x)^2$, the function is defined for all real numbers except 0. And for $f(x) = e^{2xlog(x)}$, the domain is only positive numbers.
– harshit54
Nov 17 at 13:36
1
@harshit54 Really? What is $f(x)=(x^x)^2$ for $x=-frac14$?
– Servaes
Nov 17 at 13:38
@Servaes Okay, sorry. So it's defined for all positive reals, and negative integers.
– harshit54
Nov 17 at 14:02
add a comment |
up vote
2
down vote
favorite
up vote
2
down vote
favorite
What is the domain of $f(x)=x^{2x}$?
If $f(x)=(x^2)^x $then $f$ is defined for every real number but if $f(x)=(x^x)^2$ then $f$ is only defined and "nice" (excluding the negative $-p/q$ fractions) for positive real numbers.
Should we say $f(x)=e^{2xlog(x)}$ is only defined for positive $x$?
Thanks
calculus functions
asked Nov 17 at 12:51
Pedro
510212
What is the domain of $f(x)=x^{2x}$?
If $f(x)=(x^2)^x $then $f$ is defined for every real number but if $f(x)=(x^x)^2$ then $f$ is only defined and "nice" (excluding the negative $-p/q$ fractions) for positive real numbers.
Should we say $f(x)=e^{2xlog(x)}$ is only defined for positive $x$?
Thanks
calculus functions
calculus functions
asked Nov 17 at 12:51
Pedro
510212
asked Nov 17 at 12:51
Pedro
510212
asked Nov 17 at 12:51
Pedro
510212
asked Nov 17 at 12:51
Pedro
510212
asked Nov 17 at 12:51
Pedro
510212
510212
For $f(x)=(x^x)^2$, the function is defined for all real numbers except 0. And for $f(x) = e^{2xlog(x)}$, the domain is only positive numbers.
– harshit54
Nov 17 at 13:36
1
@harshit54 Really? What is $f(x)=(x^x)^2$ for $x=-frac14$?
– Servaes
Nov 17 at 13:38
@Servaes Okay, sorry. So it's defined for all positive reals, and negative integers.
– harshit54
Nov 17 at 14:02
add a comment |
For $f(x)=(x^x)^2$, the function is defined for all real numbers except 0. And for $f(x) = e^{2xlog(x)}$, the domain is only positive numbers.
– harshit54
Nov 17 at 13:36
1
@harshit54 Really? What is $f(x)=(x^x)^2$ for $x=-frac14$?
– Servaes
Nov 17 at 13:38
@Servaes Okay, sorry. So it's defined for all positive reals, and negative integers.
– harshit54
Nov 17 at 14:02
For $f(x)=(x^x)^2$, the function is defined for all real numbers except 0. And for $f(x) = e^{2xlog(x)}$, the domain is only positive numbers.
– harshit54
Nov 17 at 13:36
For $f(x)=(x^x)^2$, the function is defined for all real numbers except 0. And for $f(x) = e^{2xlog(x)}$, the domain is only positive numbers.
– harshit54
Nov 17 at 13:36
1
1
@harshit54 Really? What is $f(x)=(x^x)^2$ for $x=-frac14$?
– Servaes
Nov 17 at 13:38
@harshit54 Really? What is $f(x)=(x^x)^2$ for $x=-frac14$?
– Servaes
Nov 17 at 13:38
@Servaes Okay, sorry. So it's defined for all positive reals, and negative integers.
– harshit54
Nov 17 at 14:02
@Servaes Okay, sorry. So it's defined for all positive reals, and negative integers.
– harshit54
Nov 17 at 14:02
add a comment |
1 Answer
1
active
oldest
votes
up vote
1
down vote
accepted
I would say that it's defined only for positive numbers. Let's look at a simpler problem: what is the domain of $x^frac12$? I can say "I could always write it as $(x^2)^frac14$." The issue is order of operations. Unless you have parantheses, you need to calculate the exponent first. See for example https://en.wikipedia.org/wiki/Order_of_operations#Serial_exponentiation
answered Nov 17 at 14:11
Andrei
10.2k21025
Nice example! Thanks
– Pedro
Nov 17 at 15:44
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
I would say that it's defined only for positive numbers. Let's look at a simpler problem: what is the domain of $x^frac12$? I can say "I could always write it as $(x^2)^frac14$." The issue is order of operations. Unless you have parantheses, you need to calculate the exponent first. See for example https://en.wikipedia.org/wiki/Order_of_operations#Serial_exponentiation
answered Nov 17 at 14:11
Andrei
10.2k21025
Nice example! Thanks
– Pedro
Nov 17 at 15:44
add a comment |
up vote
1
down vote
accepted
I would say that it's defined only for positive numbers. Let's look at a simpler problem: what is the domain of $x^frac12$? I can say "I could always write it as $(x^2)^frac14$." The issue is order of operations. Unless you have parantheses, you need to calculate the exponent first. See for example https://en.wikipedia.org/wiki/Order_of_operations#Serial_exponentiation
answered Nov 17 at 14:11
Andrei
10.2k21025
Nice example! Thanks
– Pedro
Nov 17 at 15:44
add a comment |
up vote
1
down vote
accepted
up vote
1
down vote
accepted
I would say that it's defined only for positive numbers. Let's look at a simpler problem: what is the domain of $x^frac12$? I can say "I could always write it as $(x^2)^frac14$." The issue is order of operations. Unless you have parantheses, you need to calculate the exponent first. See for example https://en.wikipedia.org/wiki/Order_of_operations#Serial_exponentiation
answered Nov 17 at 14:11
Andrei
10.2k21025
I would say that it's defined only for positive numbers. Let's look at a simpler problem: what is the domain of $x^frac12$? I can say "I could always write it as $(x^2)^frac14$." The issue is order of operations. Unless you have parantheses, you need to calculate the exponent first. See for example https://en.wikipedia.org/wiki/Order_of_operations#Serial_exponentiation
answered Nov 17 at 14:11
Andrei
10.2k21025
answered Nov 17 at 14:11
Andrei
10.2k21025
answered Nov 17 at 14:11
Andrei
10.2k21025
answered Nov 17 at 14:11
Andrei
10.2k21025
10.2k21025
Nice example! Thanks
– Pedro
Nov 17 at 15:44
add a comment |
Nice example! Thanks
– Pedro
Nov 17 at 15:44
Nice example! Thanks
– Pedro
Nov 17 at 15:44
Nice example! Thanks
– Pedro
Nov 17 at 15:44
add a comment |
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For $f(x)=(x^x)^2$, the function is defined for all real numbers except 0. And for $f(x) = e^{2xlog(x)}$, the domain is only positive numbers.
– harshit54
Nov 17 at 13:36
1
@harshit54 Really? What is $f(x)=(x^x)^2$ for $x=-frac14$?
– Servaes
Nov 17 at 13:38
@Servaes Okay, sorry. So it's defined for all positive reals, and negative integers.
– harshit54
Nov 17 at 14:02