A function sum with a bump
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Is there a function, $f(x)$, concave up on the interval $[-1,1]$, such that $f(-x)+f(x)$ looks like a "w" centered at zero within $[-1,1]$ (I.e. it has a bump at zero). If so, what is that function?
functions graphing-functions
asked Jan 7 at 18:34
Caleb DevineCaleb Devine
1084
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add a comment |
$begingroup$
Is there a function, $f(x)$, concave up on the interval $[-1,1]$, such that $f(-x)+f(x)$ looks like a "w" centered at zero within $[-1,1]$ (I.e. it has a bump at zero). If so, what is that function?
functions graphing-functions
asked Jan 7 at 18:34
Caleb DevineCaleb Devine
1084
$endgroup$
add a comment |
$begingroup$
Is there a function, $f(x)$, concave up on the interval $[-1,1]$, such that $f(-x)+f(x)$ looks like a "w" centered at zero within $[-1,1]$ (I.e. it has a bump at zero). If so, what is that function?
functions graphing-functions
asked Jan 7 at 18:34
Caleb DevineCaleb Devine
1084
$endgroup$
Is there a function, $f(x)$, concave up on the interval $[-1,1]$, such that $f(-x)+f(x)$ looks like a "w" centered at zero within $[-1,1]$ (I.e. it has a bump at zero). If so, what is that function?
functions graphing-functions
functions graphing-functions
asked Jan 7 at 18:34
Caleb DevineCaleb Devine
1084
asked Jan 7 at 18:34
Caleb DevineCaleb Devine
1084
edited Jan 7 at 18:39
Caleb Devine
asked Jan 7 at 18:34
Caleb DevineCaleb Devine
1084
asked Jan 7 at 18:34
Caleb DevineCaleb Devine
1084
asked Jan 7 at 18:34
Caleb DevineCaleb Devine
1084
1084
add a comment |
add a comment |
1 Answer
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If $f$ is concave up on $[-1,1]$, then so is $fcirc n$, where $n$ is the negation function. So $fcirc n+f$ will also be concave up on $[-1,1]$ and cannot look like a "w" (concave down near $0$).
answered Jan 7 at 18:45
alex.jordanalex.jordan
39.5k560122
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$begingroup$
If $f$ is concave up on $[-1,1]$, then so is $fcirc n$, where $n$ is the negation function. So $fcirc n+f$ will also be concave up on $[-1,1]$ and cannot look like a "w" (concave down near $0$).
answered Jan 7 at 18:45
alex.jordanalex.jordan
39.5k560122
$endgroup$
add a comment |
$begingroup$
If $f$ is concave up on $[-1,1]$, then so is $fcirc n$, where $n$ is the negation function. So $fcirc n+f$ will also be concave up on $[-1,1]$ and cannot look like a "w" (concave down near $0$).
answered Jan 7 at 18:45
alex.jordanalex.jordan
39.5k560122
$endgroup$
add a comment |
$begingroup$
If $f$ is concave up on $[-1,1]$, then so is $fcirc n$, where $n$ is the negation function. So $fcirc n+f$ will also be concave up on $[-1,1]$ and cannot look like a "w" (concave down near $0$).
answered Jan 7 at 18:45
alex.jordanalex.jordan
39.5k560122
$endgroup$
If $f$ is concave up on $[-1,1]$, then so is $fcirc n$, where $n$ is the negation function. So $fcirc n+f$ will also be concave up on $[-1,1]$ and cannot look like a "w" (concave down near $0$).
answered Jan 7 at 18:45
alex.jordanalex.jordan
39.5k560122
answered Jan 7 at 18:45
alex.jordanalex.jordan
39.5k560122
answered Jan 7 at 18:45
alex.jordanalex.jordan
39.5k560122
answered Jan 7 at 18:45
alex.jordanalex.jordan
39.5k560122
39.5k560122
add a comment |
add a comment |
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