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Given : f(x) = 5x-3
To Find : check function is continuous at x = 0 , x = -3 , x = 5
Solution:
f(x) is continuous at x = a
if
Lim (x → a) f(x) = f(a)
f(x) = 5x-3
Lim (x → c) f(x) = 5c - 3
f(c) = 5c - 3
LHS = RHS
f(x) = 5x - 3 is continuous x ∈ R
Check at x = 0 , x = - 3 , x = 5
Lim (x → 0) f(x) = 5(0) - 3 = - 3
f(0) = 5(0)-3 = - 3
Lim (x → 0) f(x) = f(0)
Lim (x → -3) f(x) = 5(-3) - 3 = - 18
f(-3) = 5(-3)-3 = - 18
Lim (x → -3) f(x) = f(-3)
Lim (x → 5) f(x) = 5(5) - 3 = 22
f(5) = 5(5)-3 = 22
Lim (x → 5) f(x) = f(5)
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