Answer
$\mathrm{Neither\:even\:nor\:odd}.$
Work Step by Step
$\mathrm{Function\:Parity\:Definition:} $
$\mathrm{Even\:Function:}\:\: $ A function is even if $\ h(-t)=h(t)\ $ for all $\ x\in \mathbb{R}. $
$\mathrm{Odd\:Function:}\:\: $ A function is odd if $\ h(-t)=-h(t)\ $ for all $\ x\in \mathbb{R}. $
$h(t)=2t+1$
$h(-t)=2(-t)+1$
$h(-t)=-2t+1$
Now,
$-h(t)=-(2t+1)$
$-h(t)=-2t-1$
Since,
$h(-t) \ne h(t)\mathrm{,\:therefore\:}2t+1\mathrm{\:is\:not\:an\:even\:function}$
$h(-t)\ne -h(t)\mathrm{,\:therefore\:}2t+1\mathrm{\:is\:not\:an\:odd\:function}$
