be fun ctions defined by f (x) = [x2andndash;3] and g(x) = -x- f (x) + -4xandndash;7 - f (x), where [y] denotes the greatest integer less than or equal to y for y andisin; R. Thena)f is discontinuous exactly at three poin ts inb)fis discontinuous exactly at four points inc)g is NOT differ en tiable exactly at four poin ts ind)g is NOT differentiable exactly at five points inCorrect answer is option 'B,C'. Can you explain this answer?

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be fun ctions defined by f (x) = [x²–3] and g(x) = |x| f (x) + |4x–7 | f (x), where [y] denotes the greatest integer less than or equal to y for y ∈ R. Then

a)
f is discontinuous exactly at three poin ts in
b)
f is discontinuous exactly at four points in
c)
g is NOT differ en tiable exactly at four poin ts in
d)
g is NOT differentiable exactly at five points in

Correct answer is option 'B,C'. Can you explain this answer?

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Verified Answer

be fun ctions defined by f (x) = [x2–3] and g(x) = |x| f (x) + |...

f(x) = [x² – 3] is discontinuous at all integral points in

∴ f is discontinuous exactly at four points in

Also g (x) = (|x| + |4x- 7|)f (x)

Here f is not differentiable at

and |x| + |4x – 7| is not differentiable at 0 and 7/4

∴ g(x) becomes differentiable at x = 7/4

Hence g(x) is non-differentiable at four points i.e.

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be fun ctions defined by f (x) = [x2–3] and g(x) = |x| f (x) + |4x–7 | f (x), where [y] denotes the greatest integer less than or equal to y for y ∈ R. Thena)f is discontinuous exactly at three poin ts inb)fis discontinuous exactly at four points inc)g is NOT differ en tiable exactly at four poin ts ind)g is NOT differentiable exactly at five points inCorrect answer is option 'B,C'. Can you explain this answer?

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