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

Answers (1)

Given function is
f ( x) = 5 x -3
f(0) = 5(0)-3 = -3
\lim_{x\rightarrow 0} f(x) = 5(0)-3 = -3
\lim_{x\rightarrow 0} f(x) =f(0)
Hence, function is continous at x = 0

f(-3)= 5(-3)-3=-15-3=-18\\\Rightarrow \lim_{x\rightarrow -3} f(x) = 5(-3)-3 = -15-3=-18\\\Rightarrow \lim_{x\rightarrow -3} f(x) = f(-3)
Hence, function is continous at x = -3

f(5)= 5(5)-3=25-3=22\\\Rightarrow \lim_{x\rightarrow 5} f(x) = 5(5)-3 = 25-3=-22\\ \Rightarrow \lim_{x\rightarrow 5} f(x) = f(5)
Hence, fucnction is continous at x = 5

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