If the function f x - is continuous in - 0-3- where f x - 3x - 4- for 0 - x - 2 - 2x - k- for 2 - x - 3Find the value of constant k-

f(2)=3(2) 4=2 lim _ h→ 0 f(2 h) =3(2 h) 4 =6 3h 4 =2 lim _ h→ 0 f(2+h) =2(2+h)+k =4+2h+k =4+k Since f( x ) is co ...

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Continuity of a Function

If the functi...

Question

If the function $f (x)$ , is continuous in $[0, 3]$ where
$f (x) = 3 x - 4,$ for $0 \leq x \leq 2$
$= 2 x + k,$ , for $2 < x \leq 3$
Find the value of constant k.

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Solution

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Similar questions

f (x)

x = 0

f (x) = \frac{8^{x} - 2^{x}}{k^{x} - 1}

x \neq 0

= 2,

x = 0

k

f (x) = \frac{8^{x} - 2^{x}}{k^{x} - 1},

x \neq 0

= 2,

x = 0

k

x = 2

f (x) = ⎧ ⎨ ⎩ \begin{matrix} \begin{matrix} 2 x + 1, k, \end{matrix} 3 x - 1, \end{matrix} \begin{matrix} if x < 2 if x = 2 if x > 2 \end{matrix}

f (x)

x = 0

f (x) = \frac{8^{x} - 2^{x}}{k^{k} - 1}

x \neq 0

= 12

x = 0

k

f (x)

[- 2, 2]

(a + b)

f (x) = \frac{sin a x}{x} - 2,

- 2 \leq x < 0

= 2 x + 1,

0 \leq x \leq 1

= 2 b \sqrt{x^{2} + 3 - 1},

1 < x \leq 2

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