Question

The function f:R→R.given by fx =ln|x+√(1+x^2)| is neither even nor odd.true or false

Answer 1

any function is even when
f(x ) = f (- x )
or function is odd only when
f(x ) = -f( -x )

now ,
given f( x ) = ln | x +√(1+x^2) |
take x = -x

f( -x ) =ln | -x +√(1 + x^2) |
add f (x ) and f (-x )

f(x )+f(-x )=ln| x +√(1+x^2)| +ln| -x +√(1+x^2)|

=ln{(√(1+x^2)^2-x^2 }

=ln {1 + x^2 -x ^2 }

=ln1 = 0
hence,
f(x ) + f (-x ) = 0
f(x ) = - f( -x )
so, f(x ) is odd function .
statement is wrong that f(x ) is neither even nor odd .