Question

Consider the graph of the function $f(x)=e^{\ln \left(\frac{x+1}{}\right)}$. Then which of the following is correct.

• A. range of the function is $(1,\infty )$
• B. $f(x)$ has no zeroes.
• C. graph lies completely above the $x$-axis.
• D. domain of $f$ is $(-\infty ,-3)\cup (-1,\infty )$

Answer 1

Answer: (B), (C), (D)

$y=\frac{x+3}{x+1}>0$
$\Rightarrow x<-3\text{ or }x>-1$
$\text{ as }x\to -3,y\to 0;x\to \pm \infty ,y\to 1$
$\text{ range }(0,1)\cup (1,\infty )$