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Which of the following statements is true for the function f(x) = {x² + 3, x ≠ 0; 1, x = 0} ?
The number of points of discontinuity of f(x) = {|x|+3, if x ≤ –3; –2x, if –3 < x < 3; 6x+2, if x ≥ 3} is :
A function f(x) = |1 – x + |x|| is :
If x = e^(x/y), prove that dy/dx = (log x – 1)/(log x)²
Check the differentiability of f(x) = {x² + 1, 0 ≤ x < 1; 3 – x, 1 ≤ x ≤ 2} at x = 1.
Find the value of a and b so that function f defined as : f(x) = {(x – 2)/(|x – 2|) + a, if x < 2; a + b, if x = 2; (x – 2)/(|x – 2|) + b, if x > 2} is a continuous function.
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