- #1
ice109
- 1,714
- 6
is the set of all functions a ... (blank), i don't know what the correct classification is, but it should contain the property of the multiplicative inverse. that's basically what the question is. does the set of all (really all) functions contain these two properties:
[tex] f=f[/tex]
and
[tex] f \frac{1}{f} =1[/tex]
for example for polynomial functions this is true
[tex]f(x)=x[/tex]
[tex]f(x)\left(\frac{1}{f(x)}\right)=\frac{x}{x}=1[/tex]
at least so I've been taught since the beginning of time.
but the question is does this hold true for ALL functions. basically what kind of set is the set of all functions.
[tex] f=f[/tex]
and
[tex] f \frac{1}{f} =1[/tex]
for example for polynomial functions this is true
[tex]f(x)=x[/tex]
[tex]f(x)\left(\frac{1}{f(x)}\right)=\frac{x}{x}=1[/tex]
at least so I've been taught since the beginning of time.
but the question is does this hold true for ALL functions. basically what kind of set is the set of all functions.