Me and my graphing calculator disagree with Wolfram Alpha's result concerning the following function
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$$frac{x - arcsin(2 x)}{x^{0.6} tanh(3 x)} $$
Can you help me make sure which is the correct domain? Why does Wolfram Alpha remove the part on the left despite it being in the domain?
I got the domain for this function by intersecting the domains of each of the smaller functions inside it and it was from -1/2 to 1/2 where x is never equal to zero , I checked the graph of the function using Desmos app and it showed me a graph having the same domain I solved , but when I did the same on Wolfram Alpha it showed that the domain is from 0 to 1/2 (excluding zero) , I am sure of my calculations but I don't understand why does Wolfram Alpha show me this false graph , domain
calculus algebra-precalculus graphing-functions
edited Nov 25 at 20:25
amWhy
191k28223439
asked Nov 25 at 17:21
user597368
62
|
show 3 more comments
up vote
0
down vote
favorite
$$frac{x - arcsin(2 x)}{x^{0.6} tanh(3 x)} $$
Can you help me make sure which is the correct domain? Why does Wolfram Alpha remove the part on the left despite it being in the domain?
I got the domain for this function by intersecting the domains of each of the smaller functions inside it and it was from -1/2 to 1/2 where x is never equal to zero , I checked the graph of the function using Desmos app and it showed me a graph having the same domain I solved , but when I did the same on Wolfram Alpha it showed that the domain is from 0 to 1/2 (excluding zero) , I am sure of my calculations but I don't understand why does Wolfram Alpha show me this false graph , domain
calculus algebra-precalculus graphing-functions
edited Nov 25 at 20:25
amWhy
191k28223439
asked Nov 25 at 17:21
user597368
62
8
You are missing a few crucial pieces of information. Namely, what do your calculators and Wolfram Alpha "tell" you? (And what do you think about which one is correct?)
– Clement C.
Nov 25 at 17:29
1
What's $(-1)^{0.6}$? It depends on whether you compute it as $(-1)^{6/10}$ or $(-1)^{3/5}$. Raising to a non integer power is only sensibly defined for positive base.
– egreg
Nov 25 at 17:38
@ClementC. Sure
– user597368
Nov 25 at 17:43
@egreg Oh , I didn't know about that so you are telling me that the domains of x^(3/5) , x^(6/10) , x^(0.6) are in some way different?
– user597368
Nov 25 at 17:45
In math, once beyond certain level, raising a negative number to a non-integral power will be treated as a complex number. The domain for $x^{3/5}, x^{6/10}, x^{0.6}$ (as a real function) all becomes $(0,infty)$. The only exception is when handling some algebra problem, one may (but not must) treat fractional power written out explicitly as a quotient of two odd number differently. e.g. $(-1)^{3/5} = -1$ but $(-1)^{6/10} = (-1)^{0.6} = e^{frac{3pi}{5} i}$ (for the default branch). So WA is right, Desmos is probably wrong. Your calculator may be right because of its targeted base of users.
– achille hui
Nov 25 at 18:27
|
show 3 more comments
up vote
0
down vote
favorite
up vote
0
down vote
favorite
$$frac{x - arcsin(2 x)}{x^{0.6} tanh(3 x)} $$
Can you help me make sure which is the correct domain? Why does Wolfram Alpha remove the part on the left despite it being in the domain?
I got the domain for this function by intersecting the domains of each of the smaller functions inside it and it was from -1/2 to 1/2 where x is never equal to zero , I checked the graph of the function using Desmos app and it showed me a graph having the same domain I solved , but when I did the same on Wolfram Alpha it showed that the domain is from 0 to 1/2 (excluding zero) , I am sure of my calculations but I don't understand why does Wolfram Alpha show me this false graph , domain
calculus algebra-precalculus graphing-functions
edited Nov 25 at 20:25
amWhy
191k28223439
asked Nov 25 at 17:21
user597368
62
$$frac{x - arcsin(2 x)}{x^{0.6} tanh(3 x)} $$
Can you help me make sure which is the correct domain? Why does Wolfram Alpha remove the part on the left despite it being in the domain?
I got the domain for this function by intersecting the domains of each of the smaller functions inside it and it was from -1/2 to 1/2 where x is never equal to zero , I checked the graph of the function using Desmos app and it showed me a graph having the same domain I solved , but when I did the same on Wolfram Alpha it showed that the domain is from 0 to 1/2 (excluding zero) , I am sure of my calculations but I don't understand why does Wolfram Alpha show me this false graph , domain
calculus algebra-precalculus graphing-functions
calculus algebra-precalculus graphing-functions
edited Nov 25 at 20:25
amWhy
191k28223439
asked Nov 25 at 17:21
user597368
62
edited Nov 25 at 20:25
amWhy
191k28223439
asked Nov 25 at 17:21
user597368
62
edited Nov 25 at 20:25
amWhy
191k28223439
edited Nov 25 at 20:25
amWhy
191k28223439
edited Nov 25 at 20:25
amWhy
191k28223439
191k28223439
asked Nov 25 at 17:21
user597368
62
asked Nov 25 at 17:21
user597368
62
asked Nov 25 at 17:21
user597368
62
62
8
You are missing a few crucial pieces of information. Namely, what do your calculators and Wolfram Alpha "tell" you? (And what do you think about which one is correct?)
– Clement C.
Nov 25 at 17:29
1
What's $(-1)^{0.6}$? It depends on whether you compute it as $(-1)^{6/10}$ or $(-1)^{3/5}$. Raising to a non integer power is only sensibly defined for positive base.
– egreg
Nov 25 at 17:38
@ClementC. Sure
– user597368
Nov 25 at 17:43
@egreg Oh , I didn't know about that so you are telling me that the domains of x^(3/5) , x^(6/10) , x^(0.6) are in some way different?
– user597368
Nov 25 at 17:45
In math, once beyond certain level, raising a negative number to a non-integral power will be treated as a complex number. The domain for $x^{3/5}, x^{6/10}, x^{0.6}$ (as a real function) all becomes $(0,infty)$. The only exception is when handling some algebra problem, one may (but not must) treat fractional power written out explicitly as a quotient of two odd number differently. e.g. $(-1)^{3/5} = -1$ but $(-1)^{6/10} = (-1)^{0.6} = e^{frac{3pi}{5} i}$ (for the default branch). So WA is right, Desmos is probably wrong. Your calculator may be right because of its targeted base of users.
– achille hui
Nov 25 at 18:27
|
show 3 more comments
8
You are missing a few crucial pieces of information. Namely, what do your calculators and Wolfram Alpha "tell" you? (And what do you think about which one is correct?)
– Clement C.
Nov 25 at 17:29
1
What's $(-1)^{0.6}$? It depends on whether you compute it as $(-1)^{6/10}$ or $(-1)^{3/5}$. Raising to a non integer power is only sensibly defined for positive base.
– egreg
Nov 25 at 17:38
@ClementC. Sure
– user597368
Nov 25 at 17:43
@egreg Oh , I didn't know about that so you are telling me that the domains of x^(3/5) , x^(6/10) , x^(0.6) are in some way different?
– user597368
Nov 25 at 17:45
In math, once beyond certain level, raising a negative number to a non-integral power will be treated as a complex number. The domain for $x^{3/5}, x^{6/10}, x^{0.6}$ (as a real function) all becomes $(0,infty)$. The only exception is when handling some algebra problem, one may (but not must) treat fractional power written out explicitly as a quotient of two odd number differently. e.g. $(-1)^{3/5} = -1$ but $(-1)^{6/10} = (-1)^{0.6} = e^{frac{3pi}{5} i}$ (for the default branch). So WA is right, Desmos is probably wrong. Your calculator may be right because of its targeted base of users.
– achille hui
Nov 25 at 18:27
8
8
You are missing a few crucial pieces of information. Namely, what do your calculators and Wolfram Alpha "tell" you? (And what do you think about which one is correct?)
– Clement C.
Nov 25 at 17:29
You are missing a few crucial pieces of information. Namely, what do your calculators and Wolfram Alpha "tell" you? (And what do you think about which one is correct?)
– Clement C.
Nov 25 at 17:29
1
1
What's $(-1)^{0.6}$? It depends on whether you compute it as $(-1)^{6/10}$ or $(-1)^{3/5}$. Raising to a non integer power is only sensibly defined for positive base.
– egreg
Nov 25 at 17:38
What's $(-1)^{0.6}$? It depends on whether you compute it as $(-1)^{6/10}$ or $(-1)^{3/5}$. Raising to a non integer power is only sensibly defined for positive base.
– egreg
Nov 25 at 17:38
@ClementC. Sure
– user597368
Nov 25 at 17:43
@ClementC. Sure
– user597368
Nov 25 at 17:43
@egreg Oh , I didn't know about that so you are telling me that the domains of x^(3/5) , x^(6/10) , x^(0.6) are in some way different?
– user597368
Nov 25 at 17:45
@egreg Oh , I didn't know about that so you are telling me that the domains of x^(3/5) , x^(6/10) , x^(0.6) are in some way different?
– user597368
Nov 25 at 17:45
In math, once beyond certain level, raising a negative number to a non-integral power will be treated as a complex number. The domain for $x^{3/5}, x^{6/10}, x^{0.6}$ (as a real function) all becomes $(0,infty)$. The only exception is when handling some algebra problem, one may (but not must) treat fractional power written out explicitly as a quotient of two odd number differently. e.g. $(-1)^{3/5} = -1$ but $(-1)^{6/10} = (-1)^{0.6} = e^{frac{3pi}{5} i}$ (for the default branch). So WA is right, Desmos is probably wrong. Your calculator may be right because of its targeted base of users.
– achille hui
Nov 25 at 18:27
In math, once beyond certain level, raising a negative number to a non-integral power will be treated as a complex number. The domain for $x^{3/5}, x^{6/10}, x^{0.6}$ (as a real function) all becomes $(0,infty)$. The only exception is when handling some algebra problem, one may (but not must) treat fractional power written out explicitly as a quotient of two odd number differently. e.g. $(-1)^{3/5} = -1$ but $(-1)^{6/10} = (-1)^{0.6} = e^{frac{3pi}{5} i}$ (for the default branch). So WA is right, Desmos is probably wrong. Your calculator may be right because of its targeted base of users.
– achille hui
Nov 25 at 18:27
|
show 3 more comments
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8
You are missing a few crucial pieces of information. Namely, what do your calculators and Wolfram Alpha "tell" you? (And what do you think about which one is correct?)
– Clement C.
Nov 25 at 17:29
1
What's $(-1)^{0.6}$? It depends on whether you compute it as $(-1)^{6/10}$ or $(-1)^{3/5}$. Raising to a non integer power is only sensibly defined for positive base.
– egreg
Nov 25 at 17:38
@ClementC. Sure
– user597368
Nov 25 at 17:43
@egreg Oh , I didn't know about that so you are telling me that the domains of x^(3/5) , x^(6/10) , x^(0.6) are in some way different?
– user597368
Nov 25 at 17:45
In math, once beyond certain level, raising a negative number to a non-integral power will be treated as a complex number. The domain for $x^{3/5}, x^{6/10}, x^{0.6}$ (as a real function) all becomes $(0,infty)$. The only exception is when handling some algebra problem, one may (but not must) treat fractional power written out explicitly as a quotient of two odd number differently. e.g. $(-1)^{3/5} = -1$ but $(-1)^{6/10} = (-1)^{0.6} = e^{frac{3pi}{5} i}$ (for the default branch). So WA is right, Desmos is probably wrong. Your calculator may be right because of its targeted base of users.
– achille hui
Nov 25 at 18:27