Let f(x) = max (2x + 1, 3 − 4x), where x is any real number. Then the minimum possible value of f(x) is:
Explanation:
Let the two lines represent the equations y = 2x + 1 and y = 3 – 4x
f(x) = max{2x + 1, 4 - 3x} is represented by green and blue lines.
f(x) is greater than 5/3, when x < 1/3 (green part) or x > 1/3 (blue part).
∴ f(x) is minimum at x = 1/3 and this value is 5/3.
Hence, option (e).
Note: The minimum value of the function f(x) = max (ax + b, cx + d) occurs when ax + b = cx + d (Only if one line has a positive slope and the other one has a negative slope)
» Your doubt will be displayed only after approval.
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.