I want to know if it is still a convex function after function composition?

![58c8aaa7802a357eb0a2646fc088eca|690x216](upload://mGQxLBdeoQcvWIdvRxouGWT271u.png

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It has been proved that expression 1 is a convex function, where X1 and X2 are variables. When we replace X1 with the square of X1 and X2 with the square of X2, is the new expression convex?
thx

No, you can specialize formula (2) to produce expressions which look like -\log{(1+x^2)}, which is neither convex nor concave.

Thank you. It seems that the way I want to convert the problem to convex optimization is not feasible