Fx - x 2 -16 x-4 -a for x4 is continuous at x-4- find a and b-

x → 4^ lim f(x) = f(4) = x + 4^+lim f(x) ⇒x + 4^ lim(x 4) (x + 4)(x 4) + a = 2 = x → 4^+lim 3x^2 + 4x + b ⇒ a + 8 = 2 = 48 + 16 + b ∴ a ...

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Definition of Functions

fx = x 2 -16 ...

Question

$f (x) \begin{matrix} = \frac{x^{2} - 16}{x - 4} + a f o r x < 4 = 2, f o r x = 4 = 3 x^{2} + 4 x + b, f o r x > 4 \end{matrix}$ is continuous at $x = 4$ , find $a$ and $b$ .

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f (x) = \{\begin{matrix} \frac{x - 4}{|x - 4|} + a, if & x < 4 \\ a + b, if & x = 4 \\ \frac{x - 4}{|x - 4|} + b, if & x > 4 \end{matrix}

f (x) = \{\begin{matrix} \frac{x - 4}{|x - 4|} + a, & x < 4 \\ a + b, & x = 4 \\ \frac{x - 4}{|x - 4|} + b, & x > 4 \end{matrix}

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