Question

Question 1: Prove that the function f (x) = 5x – 3 is continuous at x = 0, at x = – 3 and at x = 5.

Class 12 - Math - Continuity and Differentiability

Answer 1

Given function is
f(x) = 5x-3

Now at x = 0
f(x) = 5(0) -3 => -3

limx→0 5(x)-3 = -3

therefore limx→0 f(x) = f(0) hence function in continuous at x = 0
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Now At x = -3

f(-3)
= 5(-3)-3 = -18

now lim x→-3 f(x) = 5(-3)-3
= -18
thus f(-3) = limx→-3 f(x)
hence function Is continuous at x = -3

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Now at x = 5
f(x) = f(5) = 5(5)-3
= 22

also lim x→5 f(x) = lim x→5 5x-3
= 5(5) - 3 => 22

Thus f(5) = lim x→5 f(x)
hence function is continuous at x = 5