Let f : R $ \to $ R be a function defined as $$f(x) = \left\{ {\matrix{ 5 & ; & {x \le 1} \cr {a + bx} & ; & {1 < x < 3} \cr {b + 5x} & ; & {3 \le x < 5} \cr {30} & ; & {x \ge 5} \cr } } \right.$$ Then, f is

Question

Let f : R $ \to $ R be a function defined as
$$f(x) = \left\{ {\matrix{ 5 & ; & {x \le 1} \cr {a + bx} & ; & {1 < x < 3} \cr {b + 5x} & ; & {3 \le x < 5} \cr {30} & ; & {x \ge 5} \cr } } \right.$$

Then, f is

continuous if a = 0 and b = 5

continuous if a = –5 and b = 10

continuous if a = 5 and b = 5

not continuous for any values of a and b

Solution

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