Answer
$\lim\limits_{x\to-1}f(x)=f(-1)$, therefore $f(x)$ is continuous at x = -1
Work Step by Step
*NOTES TO REMEMBER: $f(x)$ is continuous at $a$ if and only if $$\lim\limits_{x\to a}f(x)=f(a)$$
We consider
$\lim\limits_{x\to-1}f(x)$
$=\lim\limits_{x\to-1}(x+2x^3)^4$
$=(-1+2\times(-1)^3)^4$
$= 81$
$f(-1)=(x+2x^3)^4$
$=(-1+2\times(-1)^3)^4$
$= 81$
When $\lim\limits_{x\to a}f(x)$, and $f(a)$ are equal, the definition of continuity is satisfied and the function is continuous at $a$.
