Let f(x)=∣∣2x2+5∣∣x|−3|,x∈R. If m and n denote the number of points where f is not continuous and not differentiable respectively, then m+n is equal to :

The function f(x) = |2x^2 + 5|/|x - 3| is a rational function where the numerator is an absolute value function and the denominator is also an absolute value function.

Step 1: Identify the points of discontinuity A rational function is discontinuous at the points where the denominator is zero. So, we set the denominator equal to zero and solve for x:

|x - 3| = 0 x = 3

So, the function is discontinuous at x = 3. Therefore, m = 1.

Step 2: Identify the points of non-differentiability A function is not differentiable at the points where it is not continuous. So, the function is not differentiable at x = 3.

In addition, the function is not differentiable at the points where the absolute value function changes from positive to negative or vice versa. This happens at the roots of the function inside the absolute value.

For the numerator, we set 2x^2 + 5 = 0 and solve for x, but this equation has no real roots.

For the denominator, we already found that the function inside the absolute value is zero at x = 3.

So, the function is not differentiable at x = 3. Therefore, n = 1.

Step 3: Add m and n m + n = 1 + 1 = 2.

So, m + n is equal to 2.