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AP EAMCET · Maths · Functions

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

  1. A \(R-\left\{-\frac{b}{2 a}\right\}\)
  2. B \(R-\left(\left\{-\frac{b}{2 a}\right\} \cup(-\infty,-1)\right)\)
  3. C \(R-\left(\left\{-\frac{b}{2 a}\right\} \cup\{x: x \geq 1\}\right)\)
  4. D \(R-(\{-b / 2 a\} \cup(-\infty,-1])\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(R-(\{-b / 2 a\} \cup(-\infty,-1])\)

Step-by-step Solution

Detailed explanation

Given function, \[ \begin{gathered} f(x)=\log \left\{a x^3+(a+b) x^2+(b+c) x+c\right\} \\ =\log \left\{\left(a x^2+b x+c\right)(x+1)\right\} \end{gathered} \] The function \(f(x)\) will be define, if…