Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Manipal MET2012MathematicsContinuity and Differentiability

If f(x)= array ll |x+2| ⁻¹(x+2) , & x -2 2 & x=-2 array . , then f(x) is

Options

  1. Acontinuous at x=-2
  2. Bnot continuous at x=-2
  3. Cdifferentiable at x=-2
  4. Dcontinuous but not derivable at x=-2 .

Correct answer

B. not continuous at x=-2

Step-by-step solution

f(x)= array cc |x+2| ⁻¹(x+2) , & x -2 2, & x=-2 array . array r _ x -2⁻ f(x)= _ h 0 f(-2-h) = _ h 0 |-2-h+2| ⁻¹(-2-h+2) array = _ h 0 -h ⁻¹ h =-1 and _ x -2⁺ f(x)= _ h 0 f(-2+h) aligned & = _ h 0 [ |-2+h+2| ⁻¹(-2+h+2) ] & = _ h 0 h ⁻¹ h =1 _ x -2⁻ f(x) & _ x -2⁺ f(x) aligned So, f(x) is not continuous as well as not differentiable at x=-2 .

Practice Continuity and Differentiability on Quantrex Academy →

More from Continuity and Differentiability

The function f(x) = |x| + |x - 1| is: 2026If f(x) = cases 1+x - 1-x x , & x 0 k, & x = 0 cases is continuous at x = 0 , then k = 2026The function y = ||x| - 1| is differentiable for all values of ' x ' except 2026Let f : R R be the function given by f(x) = |x - 2| + 3|x - 1| + ||x - 2| - 1| . What is the number of points where f is NOT differentiable? 2026For real numbers a and b , consider the function f : R R given by f(x) = cases -ax - b & if x 1. cases How many pairs (a, b) are there for which f is continuous at every point of R 2026If f(x) = cases ax + 7 & if x 1 cases is continuous at x = 1 , then 2026If the function f(x) defined by f(x) = cases ax + 1 & if x 3 bx + 3 & if x > 3 cases is continuous at x = 3 , then (a - b) = .......... 2026Let [x] denotes the greatest integer less than or equal to x and f(x) = [ ^2 x] , then which of the following is true ? 2026 Full Continuity and Differentiability list All Manipal MET PYQs