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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
Prove that the function f(x) = 5x − 3 is continuous at x = 0, x = −3 and at x = 5
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) = 5x − 3
At x = 0,
f(0) = 5(0) − 3 = −3
limx→0 f(x) = limx→0 (5x − 3)
= 5(0) −3 = −3
⇒ limx→0 f(x) = f(0)
Therefore,
f is continous at x = 0
At x = −3,
f(−3) = 5(−3) − 3 = −18
limx→−3 f(x) = limx→−3 (5x − 3)
= 5(−3) − 3 = −18
⇒ limx→−3 f(x) = f(−3)
Therefore,
f is continous at x = −3.
At x = 5,
f(5) = 5(5) − 3 = 22
limx→5 f(x) = limx→5 (5x − 3) = 5(5) − 3 = 22
⇒ limx→5 f(x) = f(5)
Therefore, f is continous at x = 5
NCERT Solutions Class 12 Maths - Chapter 5 Exercise 5.1 Question 1
Prove that the function f(x) = 5x − 3 is continuous at x = 0, x = −3 and at x = 5
Summary:
The function f(x) = 5x − 3 is continuous at x = 0, x = −3 and at x = 5
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