Find the values of k so that the function f is continuous at the indicated point. ,, at x f(x)={kx +1,ifx≤53x-5,ifx>5 at x =5 - Mathematics

Question

Find the values of k so that the function f is continuous at the indicated point.

$f (x) = {\begin{cases} k x + 1 & , if x \leq 5 \\ 3 x - 5 & , if x > 5 \end{cases} at x = 5$

Sum

Solution

$f (x) = {\begin{cases} kx + 1, if x \leq 5 \\ 3 x - 5, if x > 5 \end{cases}$

If f(x) is continuous at x = 5, this implies:

$f (5) = lim_{x \to 5^{+}} f (x) = lim_{x \to 5^{-}} f (x)$

$\Rightarrow k (5) + 1 = 3 (5) - 5 = k (5) + 1$

$\Rightarrow k (5) + 1 = 3 (5) - 5$

$\Rightarrow k (5) = 9$

$\Rightarrow k = \frac{9}{5}$

That is, for the quantity $k = \frac{9}{5}$ this function is continuous at x = 5.

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Algebra of Continuous Functions

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Chapter 5: Continuity and Differentiability - Exercise 5.1 [Page 161]

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Chapter 5 Continuity and Differentiability
Exercise 5.1 | Q 29 | Page 161

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