Question

f(x)={x²+1 if x≤2

{(x-3)² if x≥2

They said
Lim x=>2^(-) f(x)=?
lim x=> 2^+ f(x)=?

But I don't know how

Answer 1

since f(x) is defined for x=2, it is just 2^2+1 = 5

for x>2, the limit would be (2-3)^2 = 1

Since the limits are not the same, you cannot have both
f(x)={x²+1 if x≤2
{(x-3)² if x≥2

it must be either
f(x)={x²+1 if x≤2
{(x-3)² if x>2

or

f(x)={x²+1 if x<2
{(x-3)² if x≥2