Mathematics - Functions Question with Solution | TestHub

For fixed values of $a$ and $b$, $f(x)=ax+b$ is a straight line. But given $f(1)\le f(2)$ and $f(3)\ge f(4)$,

$$\begin{array}{rl}& \therefore f(1)=f(2)=f(3)=f(4)=\lambda \\ & \Rightarrow f(x)\text{ should be a constant function }\\ & \Rightarrow a=0\\ & \Rightarrow f(x)=b\\ & \Rightarrow f(\sqrt{2}r)=b\text{ and }f(\sqrt{3})=b\end{array}$$

The given expression is $\frac{n^{2}b}{b}=n^2$.