#### Question

Examine the continuity of f(x)=`x^2-x+9 "for" x-<=3`

=`4x+3 "for" x>3, at x=3`

#### Solution

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

We check the continuity at x = 3

LHL (at x=3)

= `Lim_(x→3-) f(x)`

=` lim_(h→0) f(3-h)`

=`Lim_(h→0)[(3-h)^2(3-h)+9]`

=`Lim_(h→0)[9+h^2-6h-3+h+9]=15`

`"RHL" (at x=3)=Lim_(x→3_+) f(x)=Lim_(h→0) f(3+h)`

= `Lim_(h→0) [4(3+h)+3=15]`

Also `f(3)=9-3+9=15`

Hence LHL = `f(3)=RHL`

Hence f (x) is continuous at x = 3

Is there an error in this question or solution?

#### APPEARS IN

Solution Examine the Continuity of F(X)= X 2 − X + 9 for X ⪯ 3 = 4 X + 3 for X > 3 , a T X = 3 Concept: Continuous Function of Point.