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A day full of math games & activities. Find one near you.
Find the values of k so that the function f is continuous at the indicated point f(x) = {(kx + 1, if x ≤ 5) (3x − 5, if x > 5) at x = 5
Solution:
The given function is
f(x) = {(kx + 1, if x ≤ 5) (3x − 5, if x > 5)
The given function f is continuous at x = 5,
if f is defined at x = 5 and if the value of the f at x = 5 equals the limit of f at x = 5.
It is evident that f is defined at x = 5 and
f(5) = kx + 1
= 5k + 1
limx→5- f(x) = limx→5+ f(x)
= f(5)
⇒ limx→5- (kx + 1) = limx→5+(3x − 5)
= 5k + 1
= 3(5) − 5 = 5k + 1
⇒ 5k + 1
= 15 − 5 = 5k + 1
⇒ 5k + 1 = 10
⇒ 5k = 9
⇒ k = 9/5
Therefore, the value of k = 9/5
NCERT Solutions Class 12 Maths - Chapter 5 Exercise 5.1 Question 29
Find the values of k so that the function f is continuous at the indicated point f(x) = {(kx + 1, if x ≤ 5) (3x − 5, if x > 5) at x = 5
Summary:
The value of k so that the function f is continuous at the indicated point f(x) = {(kx + 1, if x ≤ 5) (3x − 5, if x > 5) at x = 5 is 9/5
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