Question #f729c

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Answer 1 · 2017-02-13T17:24:20

It is neither, but #f(x) = ln(2-x)-ln(x+2)# is odd. (Perhaps there's a typo.)

Function #f# is even if and only if for any #x# in the domain of #f#, we have #f(-x) = f(x)#

Function #f# is odd if and only if for any #x# in the domain of #f#, we have #f(-x) = -f(x)#

The domain of the function is #(2,oo)#, so for any #x# in the domain, #-x# is not in the domain, that is, #f(-x)# is not defined.

Bonus Note

#f(x) = ln(2-x)-ln(x+2)# is odd.

The domain of #f# is #(-2,2)#.

For #x# in the domain, #-x# is also in the domain, and

#f(-x) = ln(2-(-x)) - ln((-x)+2)#

# = ln(2+x) - ln(-x+2)#

# = ln(x+2) - ln(2-x)#

#= -(ln(2-x)-ln(x+2))#

# = -f(x)#