AP EAMCET · Maths · Functions
The range of the real valued function \(f(x)=\frac{x^2+2 x-15}{2 x^2+13 x+15}\) is
- A \(\mathbb{R}-\left\{-5,-\frac{3}{2}\right\}\)
- B \(\mathbb{R}-\left\{-5, \frac{1}{2}\right\}\)
- C \(\mathbb{R}-\left\{\frac{1}{2}, \frac{8}{7}\right\}\)
- D \(\mathbb{R}-\left\{-\frac{3}{2}, \frac{8}{7}\right\}\)
Answer & Solution
Correct Answer
(C) \(\mathbb{R}-\left\{\frac{1}{2}, \frac{8}{7}\right\}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } \frac{x^2+2 x-15}{2 x^2+13 x+15}=y \\ & \Rightarrow(2 y-1) x^2+(13 y-2) x+15 y+15=0 \\ & \Rightarrow 2 y-1 \neq 0 \Rightarrow y \neq \frac{1}{2} \\ & \text { Discriminant }\gt0 \\ & \Rightarrow(13 y-2)^2-60(y+1)(2 y-1)\gt0 \\ & \Rightarrow(7…
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