AP EAMCET · Maths · Functions
The range of the function \(f(x)=\frac{x}{x^2-5 x+9}\) is
- A \(\left[\frac{1}{11}, 1\right]\)
- B \(\left[\frac{-1}{11}, 1\right]\)
- C \(\left[-1, \frac{-1}{11}\right]\)
- D \(\left[-1, \frac{1}{11}\right]\)
Answer & Solution
Correct Answer
(B) \(\left[\frac{-1}{11}, 1\right]\)
Step-by-step Solution
Detailed explanation
Given, \(f(x)=\frac{x}{x^2-5 x+9}=y\) (say) \(\begin{aligned} & \Rightarrow \quad x^2 y-5 x y+9 y=x \\ & \Rightarrow \quad x^2 y-(5 y+1) x+9 y=0\end{aligned}\) For \(x \in R, D \geq 0\)…
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