Question

Function $\frac{e^{2x}-1}{e^{2x}+1}$ is

• A. increasing
• B. decreasing
• C. neither increasing nor decreasing
• D. none of these

Answer 1

Answer: (A)

increasing

$y^{\prime }$
$=\frac{(e^{2x}+1).2.e^{2x}-2.e^{2x}(e^{2x}-1)}{(e^{2x}+1{)}^2}$
$=2e^{2x}\frac{2}{(e^{2x+1}{)}^2}$
Hence
$y^{\prime }>0$ for all real values of $x$.
Hence $y=f\left(x\right)$ is an increasing function for all real values of $x$.