Given,

…(1)

We need to check its continuity at x = 2

A function f(x) is said to be continuous at x = c if,

Left hand limit(LHL at x = c) = Right hand limit(RHL at x = c) = f(c).

Mathematically we can represent it as-

Where h is a very small number very close to 0 (h→0)

Now according to above theory-

f(x) is continuous at x = 2 if -

Clearly,

LHL = {using equation 1}

∴ LHL = (2-0)² = 4 …(2)

Similarly, we proceed for RHL-

RHL =

∴ RHL = 3(2+0) + 5 = 11 …(3)

And,

f(2) = 3(2) + 5 = 11 …(4)

Clearly from equation 2, 3 and 4 we can say that

∴ f(x) is discontinuous at x = 2

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