125.Show that the function defined by f(x) = | cos x | is a continuous function.
Here f (x) = | cos x | Let g(x) = | x | and h(x) = cos x ∴ (g o h) (x) = g (h(x)) = g(cos x) = | cos x | Now f(x) = (g o h)(x) and g,h are both continuous functions. ∴ f is continuous function.
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126.Show that the function f defined by f(x) = |1–x+|x||, where x is any real number, is a continuous function.
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127.
Find all the points of discontinuity of f defined by f(x) =|x|–|x+1|.
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128.If f is differentiable at r = a, then prove that
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129.Let a function f r be continuous at a. Show that the function g (x) = (x - a)f(x) is differentiable at x = a.
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