Question

Let $f: R \rightarrow R$ be defined by $f(x)=\frac{x^{2}-3 x-6}{x^{2}+2 x+4}$. Then which of the following statements is(are) TRUE?

• A. $f$ is decreasing in the interval $(-2,-1)$
• B. $f$ is increasing in the interval $(1,2)$
• C. $f$ is onto
• D. Range of $f$ is $\left[-\frac{3}{2}, 2\right]$

Answer 1

Answer: (A), (B)

$f^{\prime}(x)=\frac{5 x(x+4)}{\left(x^{2}+2 x+4\right)^{2}}$
$f(0)=-\frac{3}{2}$ (point of local minima)
$f(-4)=\frac{11}{6}$ (point of local maxima)