অন্বয় এবং ডোমেন ও রেঞ্জ

Let f(x)=∣x−x1∣+∣x−x2∣f(x)=\left | x-x_{1} \right |+\left | x-x_{2} \right | where x1 and x2x_{1}~ and~ x_{2} are distinct  real numbers. Then the number of points at which f(x) is minimum is:

কাজু বাদাম

∴ \therefore Here x1<x2 x_{1}<x_2

x1<x2  f(x)=x1−x+x2−x=x1+x2−2x \begin{aligned} x_{1}<x_2 ~~ f(x) & =x_{1}-x+x_{2}-x \\ & =x_{1}+x_{2}-2 x\end{aligned}

x1<x<x2→ x_{1} <x <x_{2} \rightarrow f(x)=x−x1+x2−x=x2−x1 \begin{aligned} f(x) & =x-x_{1}+x_{2}-x =x_{2}-x_{1}\end{aligned}

x<x2→f(x)=2x−x1−x2x1<x<x2 x<x_{2} \rightarrow f(x)=2 x-x_{1}-x_{2} \\ x_{1}<x<x_2

[x1,x2]→ \left[x_{1}, x_{2}\right] \rightarrow Hence, There have more than 3 number of points at which f(x) f(x) is minimum.

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