Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202523 Apr 2025Evening ShiftMathematicsContinuity and DifferentiabilityActual

The function f (x)=2 x- |x-x^2 | is

Options

  1. Acontinuous at x=1 .
  2. Bdiscontinuous at x=1 .
  3. Cnot defined at x=1 .
  4. Ddiscontinuous at x=0 .

Correct answer

A. continuous at x=1 .

Step-by-step solution

The continuity of f(x)=2x-|x-x^2| depends on the absolute value term, which requires piecewise definition. Analyzing x - x^2 = x(1 - x) , we observe that |x - x^2| = x - x^2 for 0 x 1 where x(1 - x) 0 , and |x - x^2| = x^2 - x otherwise. This gives the piecewise form: f(x) = cases 3x - x^2 & if x 1 cases To verify continuity at x = 1 , compute f(1) = 1^2 + 1 = 2 , the left-hand limit _ x 1^- (x^2 + x) = 2 , and the right-hand limit _ x 1^+ (3x - x^2) = 2 . The equality of these values confirms continuity at x = 1 .

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 MHT CET PYQs