Home
Class 12
MATHS
Let f(x)= {:{((x+a) , x lt1),( ax^(2)+1,...

Let `f(x)= {:{((x+a) , x lt1),( ax^(2)+1, xge1):}` then f(x) is continuous at x =1 for

A

a = 0

B

a = 1

C

All `a in R`

D

No value of a

Text Solution

Verified by Experts

The correct Answer is:
C
`f(1)=a+1`
`lim_(x to 1^(-)) f(x) =lim_(x to 1^(-)) (x+a) = (1+a)`
and `lim_(x to 1^(+)) f(x) = lim_(x to 1^(+)) (ax^(2)+1) =a+1`
`:.f(x)` is continuous at x = 1, whatever .a. may be.
Promotional Banner

Similar Questions

Explore conceptually related problems

Let f(x)= {:{ (x + a , x ge 1 ) , ( ax^(2) + 1, x lt 1) :} then f(x) is derivable at x =1 , if

Let f(x) = {{:( x, if , x ge 1),( x^(2), if , x lt 1):} is f a continuous function ? Why ?

If f(x) {: (=x^(3)", if " x lt 1//2 ),(= ax^(2)", if " x ge 1//2 ):} is continuous at x=1/2 , then a = ……

Show that f (x) = ((x+1",", if x le 2),( x^(2)+1)",", if x lt 1):} is continuous at x =1

Let f(x)={{:(,(1)/(|x|),"for "|x| gt1),(,ax^(2)+b,"for "|x| lt 1):} If f(x) is continuous and differentiable at any point, then

Show that the function f(x)={:{(1-x", " x lt1),(x^2-1 ", " x ge 1):} is continuous but not differnetiable at x=1

If the function f(x)={{:(k +x, "for " x lt1),(4x+3, "for " x ge1):} is continuous at x=1 then k=

Let f(x) ={:{(x, "for", 0 le x lt1),( 3-x,"for", 1 le x le2):} Then f(x) is

Let f(x)={{:(3x^(2)-4sqrtx+1,"for",xlt1),(ax+b,"for",xge1):} If f(x) is continuous and differentiable for all real values in its domain then