Question

solve this question class 12​

Answer 1

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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