Question

        

Determine the value of ‘a’ if possible, so that the function is continuous

Solution

Correct option is

= 8

As, f (x) is continuous at x = 0.

∴  We must have 

RHL (at x = 0) = LHL (at x = 0) = f (0) 

⇒ RHL (at x = 0)   

   

Put = 0 + h

  

  

Also LHL (at x = 0)

   

Put x = 0 – h

⇒       8.

and f (0) = a.

Since f (x) is continuous at x = 0

⇒      f (0) = RHL = LHL

or      f (0) = 8

or      a = 8.

SIMILAR QUESTIONS

Q1

Let f and g be differentiable function satisfying g’ (a) = 2, g (a) = b and fog = I (identity function) Then, f’(b) is equal to:

Q2

If the function , (where [.] denotes the greatest integer function) is continuous and differentiable in (4, 6), then.

Q3

Let [.] denotes the greatest integer function and f (x) = [tan2x], then:

Q4

Let f be a real function satisfying f (x + z) = f (xf (yf (zfor all real xyz . If f (2) = 4 and f’ (0) = 3. Then find f (0) and f’ (2).

Q5

Let h(x) = min.{xx2} for every real number of x. Then:

Q6

Let f : R → R be a function defined by f (x) =  max. {xx3}. The set of all points where (x) is not differentiable is:

Q7

Let f (x) = Ï•(x) + ψ(x) and Ï•(a), ψ’(a) are finite and definite. Then:

Q8

If f (x) = x + tan and g(x) is the inverse of f (x) then g’ (x) is equal to:

Q9

If f (x) is differentiable function and (f (x). g(x)) is differentiable at x = a, then

Q10

 for all real x and y. If f ’ (0) exists and equals to –1and f (0) = 1, find f ’(x).