Functions Ques 9
- The function $f(x)=\frac{x^2+4 x+30}{x^2-8 x+18}$ is not one-to-one.
(1983, 1M)
Show Answer
Answer:
Correct Answer: 9.(True)
Solution:
$ \begin{aligned} & \text { Given, } f(x)=\frac{x^2+4 x+30}{x^2-8 x+18} \\ & \Rightarrow \quad f^{\prime}(x)=\frac{\left[\begin{array}{c} \left(x^2-8 x+18\right)(2 x+4) \\ -\left(x^2+4 x+30\right)(2 x-8) \end{array}\right]}{\left(x^2-8 x+18\right)^2} \\ & =\frac{2\left(-6 x^2-12 x+156\right)}{\left(x^2-8 x+18\right)^2}=\frac{-12\left(x^2+2 x-26\right)}{\left(x^2-8 x+18\right)^2} \\ \end{aligned} $
which shows $f^x(x)$ is positive and negative both.
$\therefore f(x)$ is many one.
Hence, given statement is true.
BETA
