# Examine the Continuity of the Following Function - Mathematics and Statistics

Sum

Examine the continuity of the following function :

{:(,,f(x)= x^2 -x+9,"for",x≤3),(,,=4x+3,"for",x>3):}}"at "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

Concept: Continuous Function of Point
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