Let f:[-2,2]→ℝ and g:[-2,2]→ℝ be functions defined by f(x)=[x²] and g(x)=|x|f(x)+|4x|f(x), where [y] denotes the greatest integer less than or equal to y for y∈ℝ. Then which of the following statements is true?

f(x)=[x²]=[x²]
= 0 if -1 ≤ x < 1
= 1 if 1 ≤ x < √2
= 2 if √2 ≤ x < √3
= 3 if √3 ≤ x < 2
= 4 if x=2
f is discontinuous exactly at x = -1, 1, √2, √3. Therefore, f is discontinuous exactly at four points in [-2, 2].
g(x) = |x|f(x) + |4x|f(x) = (|x| + |4x|)f(x)
If x ≥ 0, g(x) = 5xf(x)
If x < 0, g(x) = 3xf(x)
The points of discontinuity of f(x) are x = -1, 1, √2, √3. At these points, g(x) will also be discontinuous and non-differentiable.
Additionally, g(x) is not differentiable at x = 0 because of the absolute value terms, regardless of the continuity of f(x).
Therefore, g(x) is not differentiable at x = -1, 0, 1, √2, √3. Hence, g is not differentiable exactly at five points in [-2, 2].