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Question
Prove that the function f (x) = 5x – 3 is continuous at x = 0, at x = – 3 and at x = 5.
Solution
The given function is:
f(x) = 5x - 3
f(0) = 5(0) - 3 = -3
`lim_(x → 0) f(x) = 5(0) - 3 = -3`
`lim_(x → 0) f(x) = f(0)`
Hence, the function is continuous at x = 0
f(-3) = 5(-3) - 3
= -15 - 3
= -18
⇒ `lim_(x → -3) f(x) = 5(-3) - 3`
= -15 - 3
= -18
⇒ `lim_(x → -3) f(x) = f(-3)`
Hence , function is continous at x = -3
f(5) = 5(5) - 3
= 25 - 3
= 22
⇒ `lim_(x → 5) f(x) `
= 5(5) - 3
= 25 - 3
= -22
⇒ `lim_(x → 5) f(x) = f(5)`
Hence , function is continuous at x = 5
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