# 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
1. $(-\infty, 8)$
2. $(-\infty, 100)$
3. $(-\infty, 45)$
4. $(5, \infty)$

Choice D. $(5, \infty)$

## 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 = $(5, \infty)$

Correct Answer: $(5, \infty)$

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## More questions from Inequalities

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.