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 \rightarrow-3, y \rightarrow 0 ; x \rightarrow \pm \infty, y \rightarrow 1 $
$\text { range }(0,1) \cup(1, \infty)$