If f ( x ) = { ( x 2 - 2 x ) , if x 0 4 x + 1 , if x 0 , then which one of the following is correct?

Question

If $f (x) =$ ${\begin{matrix} λ (x^{2} - 2 x), & if x \leq 0 \\ 4 x + 1, & if x > 0 \end{matrix},$ then which one of the following is correct?

Smart Achievers · Accepted Answer

(2)

Ans. $f (x)$ is discontinuous at $x = 0$ for any value of $λ$

Explanation:

$\lim_{x \to 0^{-}} f (x) = 0$ and $\lim_{x \to 0^{+}} f (x) = 1$

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