Let the function $f(x+c)$ is $\log$-convex on interval $I$, where $c\neq 0$ is a real number. My queistion is:
Is $f(x)$ log-convex?
I know that if $f(x)$ is $\log$-convex on a certain interval, and if $c\neq 0$ is any real number, then the function $f(x+c)$ is $\log$-convex on the corresponding intervals. Thanks.
$f(x)=f(x+c-c)$ and $-c \neq 0$. So the result follows from what you know.