`f(x)=int_(e^(x))^(e^(-x))ln((1)/(t))dt`, then which of following are correct?

Options

A. f(x) is increasing on interval `(1,infty)`
B. f(x) is even function.
C. f(x) is bijective function.
D. f(x) has a vertical tangent

Answer

A, C

Explanation

`f(x)=int_(e^(x))^(e^(-x))ln((1)/(t))dt`
`f^(')(x)=-ln((1)/(e^(-x)))e^(-x)-ln((1)/(e^(x)))e^(x)`
`f^(')(x)=-xe^(-x)+xe^(2)`
`f(-x)=int_(e(-x))^(e^(x))ln((1)/(t))dt`
`impliesf(-x)=-f(x)`
`impliesf(x)` is odd function