Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET2007MathematicsContinuity and Differentiability

If f(x)= ⁻¹ ( 2 x 1+x² ) , then f(x) is differentiable on

Options

  1. A[-1,1]
  2. BR- -1,1
  3. CR-(-1,1)
  4. DNone of these

Correct answer

B. R- -1,1

Step-by-step solution

Given, f(x)= ⁻¹ ( 2 x 1+x² ) On differentiating w.r.t. x , we get aligned f^ (x) &= 1 1- ( 2 x 1+x² )² d d x ( 2 x 1+x² ) &= 1+x² (1-x² )² 2 (1-x² ) (1+x² )² aligned = 2 1+x² 1-x² |1-x² | = array l 2 1+x² , if |x| 1 array . f^ (x) does not exist for |x|=1, i e, x= 1 Hence, f(x) is differentiable on R- -1,1 .

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