Let $$f(x)=g(x)$$−$$g(a)x$$−a,x≤ag′(a), $$x=a$$,where g is a function derivable at $$x=a$$, then at $$x=a$$

Correct option is 1f is continuous

Questions

$Let f (x) = \{\begin{array}{l} \frac{g (x) - g (a)}{x - a}, x \leq a \\ g^{'} (a), x = a \end{array},where g is a function derivable at x = a, then at x=a$

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f is continuous

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detailed solution

Correct option is A

limx→af(x)=limx→ag(x)−g(a)x−a =ddxgx at x=a = g'a=fa⇒ f(x) is continuous at x=a.Hence (1) is the correct answer.

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Let f(x)=g(x)−g(a)x−a,x≤ag′(a), x=a,where g is a function derivable at x=a, then at x=a

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$Let f (x) = \{\begin{array}{l} \frac{g (x) - g (a)}{x - a}, x \leq a \\ g^{'} (a), x = a \end{array},where g is a function derivable at x = a, then at x=a$