AP EAMCET202319 May 2023Morning ShiftMathematicsContinuity and DifferentiabilityActual
If a function f(x) defined on [a, b] is discontinuous at x= (a, b) , then
Options
- A_ x ⁻ f(x)= _ x ⁺ f(x)=f( )
- B_ x ⁺ f(x) f( )
- C_ x a⁻ f(x)=f(a)
- 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.