Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
Advertisement Remove all ads

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

 

Advertisement Remove all ads

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}.
 
 
 
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

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

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×