# Algebra for CAT Preparation – Finding smallest value in a maximum function

Tuesday, March 24th, 2015

A common type of question that gets asked in CAT is when you are given a maximum function and you are supposed to find out the minimum value of the function. Actually, the concept would remain the same even if you are given a minimum function and you are supposed to find out the maximum value of the function.

To solve such kind of questions, all you need to do is to find out the point of intersection of the individual values. More often than not, that would lead to the answer. Let us look at a question that has appeared in CAT before.

Let g(x) = max (5 − x, x + 2). The smallest possible value of g(x) is
A] 4.0
B] 4.5
C] 1.5
D] None of these.

Watch the video given below for better understanding of the same.

To solve such kind of questions, in most cases, all you need to do is to equate the two values inside the function
=> 5 – x = x + 2
=> x = 3/2 = 1.5
To find out the answer to the question, we need to find out the value of g(1.5)
When we put x = 1.5, we get g(x) = max (5 – 1.5, 1.5 + 2) = max (3.5, 3.5) = 3.5
So, our answer is 3.5 Option D – None of these

I would strongly recommend that you watch the video for better understanding of the solution of the question. Do check out my Online CAT Coaching and CAT Preparation course which has 500+ video tutorials for CAT.

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