Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# Find the Domain of the Real Valued Function of Real Variable: (V) F ( X ) = X 2 + 2 X + 1 X 2 − 8 X + 12 - Mathematics

Find the domain of the real valued function of real variable:

(v)  $f\left( x \right) = \frac{x^2 + 2x + 1}{x^2 - 8x + 12}$

#### Solution

(v) Given:

$f\left( x \right) = \frac{x^2 + 2x + 1}{x^2 - 8x + 12}$
$= \frac{x^2 + 2x + 1}{x^2 - 6x - 2x + 12}$
$= \frac{x^2 + 2x + 1}{x\left( x - 6 \right) - 2\left( x - 6 \right)}$
$= \frac{x^2 + 2x + 1}{\left( x - 6 \right)\left( x - 2 \right)}$
Domain of f : Clearly,  (x) is a rational function of x as
$\frac{x^2 + 2x + 1}{x^2 - 8x + 12}$ is a rational expression.
Clearly, f (x) assumes real values for all x except for all those values of x for which x2 - 8x + 12 = 0, i.e. x = 2, 6.
Hence, domain ( f ) = R -  {2,6}.

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 3 Functions
Exercise 3.3 | Q 1.5 | Page 18