How to express x*exp(inv_pos(x)) in CVX if i want to use it in my objective function

When i want to use this expression, I always get the warning :
错误使用 .*
Disciplined convex programming error:
Cannot perform the operation: {real affine} .* {convex}
However, x*exp(inv_pos(x)) is definitely convex considering x is positive

This is an exponential cone

variables x z
{1,x,z} == exponential(1)

Then use z in place of x*exp(1/x)

I really appreciate your help, thank you so much!