Let T be exponential, and let Z=max(1,T). Find the cdf of Z.
you need to be a bit clearer on the precise density, i.e., the parameter involved with T.
Then you need to figure out what it means for
$\displaystyle P(Z\le a)=P(\max\{1,T\}\le a)$
Now if the max of two values are less than a, that means both are less than a.