Question

Let $f:(0,\infty )\to R$ be given by $f\left(x\right)={\int }_{1/x}^x{e}^{(t+\frac{1}{t})}\frac{dt}{t}$, then

• A. $f\left(x\right)$ is monotonically increasing on $[1,\infty )$
• B. $f\left(x\right)$ is monotonically decreasing on (0, 1)
• C. $f\left(x\right)+f\left(\frac{1}{x}\right)=0$, for all $x\in (0,\infty )$
• D. $f\left(2^x\right)$ is an odd function of x on R

Answer 1

Answer: (A), (C), (D)

The correct options are
A $f\left(x\right)$ is monotonically increasing on $[1,\infty )$
C $f\left(x\right)+f\left(\frac{1}{x}\right)=0$, for all $x\in (0,\infty )$
D $f\left(2^x\right)$ is an odd function of x on R