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Find the relationship between a and b so that the function f defined by f(x)={(ax + 1, if x ≤ 3) (bx + 3, if x > 3) is continous at x = 3
Solution:
A function is said to be continuous when the graph of the function is a single unbroken curve.
The given function is
f(x) = {(ax + 1, if x ≤ 3) (bx + 3, if x > 3)
For f to be continuous at x = 3, then
limx→3− f(x) = limx→3+ f(x) = f(3) …(1)
Also,
limx→3− f(x) = limx→3− (ax + 1) = 3a + 1
limx→3+ f(x) = limx→3+ (bx + 3) = 3b + 3
f(3) = 3a + 1
Therefore,
from (1), we obtain
3a + 1 = 3b + 3 = 3a + 1
⇒ 3a + 1 = 3b + 3
⇒ 3a = 3b + 2
⇒ a = b + 2/3
Therefore, the required relationship is given by, a = b + 2/3
NCERT Solutions Class 12 Maths - Chapter 5 Exercise 5.1 Question 17
Find the relationship between a and b so that the function f defined by f(x)={(ax + 1, if x ≤ 3) (bx + 3, if x > 3) is continous at x = 3
Summary:
The relationship between a and b so that the function f defined by f(x)={(ax + 1, if x ≤ 3) (bx + 3, if x > 3) is continous at x = 3 is a = b + 2/3
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