Given that f(x)= { ((−x + 1, x≤ 3_ )),((kx −8, x >3)) :} is continuous then f(5) = A 2 B 0 C −2 D −1


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Question Number 66225 by Rio Michael last updated on 11/Aug/19
$Given that f(x)= { ((−x + 1, x≤ 3_ )),((kx −8, x >3)) :} is continuous then f(5) = A 2 B 0 C −2 D −1$
$G i v e n t h a t f (x) = {\begin{cases} - x + 1, x ⩽ 3_{} \\ k x - 8, x > 3 \end{cases}$ $i s c o n t i n u o u s t h e n f (5) =$ $A 2$ $B 0$ $C - 2$ $D - 1$
Commented by Prithwish sen last updated on 11/Aug/19

$A . 2$
Commented by mathmax by abdo last updated on 11/Aug/19

$f (3) = {l i m}_{x \to 3^{+}} f (x) \Rightarrow 3 k - 8 = - 2 \Rightarrow 3 k = 6 \Rightarrow k = 2$ $\Rightarrow f (x) = 1 - x i f x ⩽ 3 a n d f (x) = 2 x - 8 i f x > 3$ $\Rightarrow f (5) = 2 \times 5 - 8 = 2$
	Answered by som(math1967) last updated on 11/Aug/19

	$3 k - 8 = - 3 + 1 \Rightarrow k = \frac{6}{3} = 2$ $f (5) = 2 \times 5 - 8 = 2$
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