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# Solution - Examine the Continuity of the Following Function - Continuous Function of Point

ConceptContinuous Function of Point

#### Question

Examine the continuity of the following function :

f(x)=x^2-x+9 , for x ≤ 3

=4x+3          for x > 3

#### Solution

Given

f(x)=x^2-x+9 , for x<=3

=4x+3        for x>3

f(3)=(3)^2-3+9=9-3+9

f(3)=15

Now lim_(x->3^-)f(x)=lim_(x->3)(x^2-x+9)

=(3)^2-(3)+9

=15

lim_(x->3^-)f(x)=lim_(x->3)(4x+3)

=4(3)+3

=15

Thus from the above

lim_(x->3^-)f(x)=lim_(x->3)f(x)=15=f(3)`

Hence function is continuous at x=3

Is there an error in this question or solution?

#### APPEARS IN

2014-2015 (March)
Question 2.1.2 | 3 marks
Solution for question: Examine the Continuity of the Following Function concept: Continuous Function of Point. For the courses HSC Commerce, HSC Commerce (Marketing and Salesmanship)
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