Question

f(x) = `{{:(3x - 8",",  "if"  x ≤ 5),(2"k"",",  "if"  x > 5):}` at x = 5

Answer 1

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`