Question

$f\left(x\right)=max\{x,x+2,3-x\}$. Then the minimum value of $f\left(x\right)$ in R is

• A. $\frac{5}{2}$
• B. $2$
• C. $\frac{3}{2}$
• D. $0$

Answer 1

Answer: (A)

$\frac{5}{2}$

Plotting graphes of functions on $x-y$ plane, we can see that
$f\left(x\right)=x+2,$
$x\ge \frac{1}{2}$
$=3-x,x<\frac{1}{2}$
Clearly the minimum value is at the point of intersection of these two segments of the straight lines
i.e.at , $x=\frac{1}{2}$
Substituting value of $x$ in the function
Hence $\frac{5}{2}$ is the minimum value of $f\left(x\right)$