Fix $\alpha ,\beta\in\mathbb R$ and define a function $f$ from $\mathbb R$ to $\mathbb R$ such that $$f(x)= \begin{cases} x^{\alpha} + 3 & \quad \text{if } x\le 1 \\ x^{\beta} + 3 & \quad \text{otherwise} \end{cases}$$

How do I prove that f is continuous?

Any hint? I am stuck.

Thank you