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Question
f(x) = `{{:(3x - 8",", "if" x ≤ 5),(2"k"",", "if" x > 5):}` at x = 5
Solution
We have, f(x) = `{{:(3x - 8",", "if" x ≤ 5),(2"k"",", "if" x > 5):}`
Since, f(x) is continuous at x = 5
∴ L.H.L. = R.H.L. = f(5)
Now, L.H.L. = `lim_(x -> 5^-) (3x - 8)`
= `lim_("h" -> 0) [3(5 - "h") - 8]`
= –15 – 8
= 7
R.H.L. = `lim_(x -> 5^+) 2"k"`
= `lim_("h" -> 0) 2"k"` = 2k
Also f(5) = 3(5) – 8 = 7
∴ 2k = 7
⇒ k = `7/2`
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