Suppose x = a ∈ R and apply the conditions of continuity of a function.

A function f(x) is said to be continuous at x = c, if all the following three conditions are met;

(i) The function is defined at x = c, that is, f(x) exists at c.

(ii) The function approaches a definite limit as x approaches c, that is, lim_{x→c} f(x) exists.

(iii) The limit of the function is equal to the value of the function when x = c, that is, lim_{x→c}f(x) = c.

(i) f(a) = 2a – 3

Since ‘a’ is a real number, therefore, the RHS of the equation is a real number. Therefore, f(x) exists at ‘a’.

(ii) . Therefore, the limit exists.

(iii)

Therefore, f(x) = x – 3 is continuous for all x ∈ R.

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