Question

Let F(x) = max {(x + 3), (7 – 2x)}. What is the minimum value of F(x) for 2 $\ge$ x $\ge$ 1

• A. 4.5
• B. 5
• C. 4.33
• D. 4.67

Answer 1

The correct option is C 4.33

Please note that we are required to find out the minimum value of F(x), but F(x) always prefer to give the maximum of the two values (i.e., (x + 3), (7 - 2x)).

Thus there is only one possible condition to get the minimum of F(x) that is when both values i.e., (x + 3) and (7 - 2x) are equal.

(x+3) = (7-2x)

3x=4

x=$\frac{4}{3}$

This satisfies the constraint of 2 $\ge$ x $\ge$ 1. Minimum value will occur at x= $\frac{4}{3}$ = max $(\frac{13}{3},\frac{13}{3})$ = $\frac{13}{3}$ = 4.33