Question

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

Answer 1

Polynomial functions are continuous at every real value of x.

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Answer 2

Answer:

Here's your answer ☺️

Step-by-step explanation:

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 

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