Question

Determine whether the function is continuous or discontinous. Justify your reasoning. If discontinuous, identify points of discontinuity.

Answer 1

@ikram002p how would i determine whether the function is continous or discontinous. and how would i justify it.

Answer 2

@mathessentials would you know how to solve this

Answer 3

the equation would be continous right

Answer 4

Okay first of all every polynomial is continuous. And f(x)=x is continous too (y=x). And if a function is continous at some point then limx->a f(x)=f(a). Remember that! So 2-x^2 is continious. In this case it's continous on x<=1 and the function is x at x<1. So let's look at what happens at 1.
lim x->1- (2-x^2)=1. We saw that function when goes to 1 from the left side(that's what 1- means) is 1. And if we take limx->1+ (x)=1 well that's just 1 as we saw. So left side and right side limit are the same. We just proved that limx->1 f(x)=1. One more thing we need to prove is that f(1)=1 which doesn't need any proving. So it's true that limx->1 f(x)=f(1) and the function is continuous on R(everywhere).