CAT Practice : Inequalities

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Range is the set of values taken by the function

Properties of Inequalities

    Q.16:Find range of f(x) = x2 – 6x + 14


  • Correct Answer
    Choice D.

Detailed Solution

Given, f(x) = x2 – 6x + 14
f(x) can be written as x2 – 6x +9 -9 + 14
=> f(x)= (x-3)2 + 5
As you can see, for whatever value of x, the term (x-3)2 is always positive. The least value it can take is zero, so the minimum value of the function is 5.
The maximum value can range until infinity.
Therefore, Range =

Correct Answer:

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Inequalities are crucial to understand many topics that are tested in the CAT. Having a good foundation in this subject will make us tackling questions in Coordinate Geometry, Functions, and most importantly in Algebra much more comfortable.