Discuss the continuity of the function/given by `f(x)=x^3+x^2-1`.

Explanation

Given

`f(x)=x^3+x^2-1`

To check continuity of `f(x)`,

We will check if it is continuous at any point `x=c`

Let c be any real number

`f` is continuous at `x=c`

if `underset(xtoc)(lim)f(x)=f(c)`


L.H.S.

`underset(xtoc)(lim)f(x)= underset(xtoc)(lim)(x^3+x^2-1)`

Putting `x=c`

`underset(xtoc)(lim)f(x)= c^3+c^2-1`


R.H.S.

`f(c)=c^3+c^2-1`


Since, L.H.S = R.H.S.

`therefore` Function is continuous at `x=c`


Thus, we can write that

`f` is continuous for `x=c`, where `c` `varepsilon` `RR`

`f` is continuous for every real number.