Question

Consider the following statements:
$1.y=\frac{e^x+e^{-x}}{2}$ is an increasing function on $[0,\infty )$.
$2.y=\frac{e^x-e^{-x}}{2}$ is an increasing function on $(-\infty ,\infty )$.
Which of the above statements is/are correct?

• A. $1$ only
• B. $2$ only
• C. Both $1$ and $2$
• D. Neither $1$ nor $2$

Answer 1

Answer: (C)

Both $1$ and $2$

$y=\frac{e^x+e^{-x}}{2}=\cosh x$

$y=\frac{e^x-e^{-x}}{2}=\sinh x$

Both are increasing functions

Hence, both the statements are correct.