Given that $a, b$ and $c$ are real numbers such that $b^2=4 a c$ and $a\gamma_0$. The maximal possible set $D \subseteq R$ on which the function $f: D \rightarrow R$ given by $f(x)=\log \left\{a x^3+(a+b) x^2+(b+c) x+c\right\}$ is defined, is

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Given that $a, b$ and $c$ are real numbers such that $b^2=4 a c$ and $a>\gamma_0$. The maximal possible set $D \subseteq R$ on which the function $f: D \rightarrow R$ given by $f(x)=\log \left\{a x^3+(a+b) x^2+(b+c) x+c\right\}$ is defined, is

Aicharya · Accepted Answer

Given function, $ \begin{gathered} f(x)=\log \left\{a x^3+(a+b) x^2+(b+c) x+cight\} \ =\log \left\{\left(a x^2+b x+cight)(x+1)ight\} \end{gathered} $ The function $f(x)$ will be define, if $ \begin{aligned} & \Rightarrow \quad\left(a x^2+b x+cight)(x+1)>0 \ & 	ext { and } \ & x+1>0 \quad\left\{\because a>0 	ext { and } b^2=4 a cight\} \ & \end{aligned} $ So, $\left\{D=x: x \in(-1, \infty)ight.$ and $\left.x 
eq-\frac{b}{2 a}ight\}$ or $ D=R-\left\{-\frac{b}{2 a}ight\} \cup(-\infty,-1] . $

Given that $a, b$ and $c$ are real numbers such that $b^2=4 a c$ and $a>\gamma_0$. The maximal possible set…

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