TS EAMCET · Maths · Functions
The range of the real valued function \(f(x)=\log _3\left(5+4 x-x^2\right)\) is
- A \((0,2)\)
- B \([0,2]\)
- C \((-\infty, 2]\)
- D \([-1,5]\)
Answer & Solution
Correct Answer
(C) \((-\infty, 2]\)
Step-by-step Solution
Detailed explanation
Let \(y=f(x)\) \(\begin{aligned} & \Rightarrow y=\log _3\left(5+4 x-x^2\right) \Rightarrow 3^y=5+4 x-x^2 \\ & \Rightarrow x^2-4 x+3^y-5=0\end{aligned}\) For \(x\) to be real, discriminant \(\geq 0\) For \(x\) to be real, discriminant \(\geq 0\)…
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