CAT 2003 Slot 1 — QA Question 16
Basics (Functions)Easy
Let g(x) = max(5 − x, x + 2). The smallest possible value of g(x) is
Answer & solution
Correct answer: None of the above
- A
4.0
- B
4.5
- C
1.5
None of the above
Solution
We have, g(x) = max(5 − x, x + 2)
We have to find the smallest value of g(x).
The lines y = 5 – x and y = x + 2 intersect each other at the point (1.5, 3.5)
For x < 1.5, 5 – x > x + 2 and 5 – x > 3.5
For x > 1.5, x + 2 > 5 – x and x + 2 > 3.5
∴ At any point other than x = 1.5, the value of g(x) is greater than 3.5
Thus the smallest possible value of g(x) = 3.5 at x = 1.5
Hence, option (d).