Consider the following statements : 1. The function $f(x)=\ln x$ increases in the interval $(0, \infty)$. 2. The function $f(x)=\tan x$ increases in the interval $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$. Which of the above statements is/are correct?

• A

  1 only
• B

  2 only
• Correct answer
  C

  Both 1 and 2
• D

  Neither 1 nor 2

Solution

(1) Graph of $f(x)=\ln (x)$
This is increasing function in the interval $(0, \infty)$. (2) Graph of $f(x)=\tan x$.
This is also increasing in $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$.

Hence, the correct answer is option: 'C'.