Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202319 May 2023Morning ShiftMathematicsContinuity and DifferentiabilityActual

If a function f(x) defined on [a, b] is discontinuous at x= (a, b) , then

Options

  1. A_ x ⁻ f(x)= _ x ⁺ f(x)=f( )
  2. B_ x ⁺ f(x) f( )
  3. C_ x a⁻ f(x)=f(a)
  4. D_ x b⁺ f(x)=f(b)

Correct answer

B. _ x ⁺ f(x) f( )

Step-by-step solution

f(x) is defined on [a, b] and discontinuous at x= (a, b) Since f(x) is discontinuous at x= (a, b) Hence option (a) will never be true but _ x f(x) f( ) is showing that f(x) is discontinuous at x= (a, b) Hence option (b) is correct. Since function is not defined for x a⁻ . Hence option (c) is incorrect. Since function is not defined when x b⁺ . Hence (d) is incorrect.

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 AP EAMCET PYQs