Question

Show that the function defined by $f\left(x\right)=\sin \left(x^2\right)$ is a continuous function.

Answer 1

Let $p\left(x\right)=\sin x;9\left(x\right)=x^2[x\in R]$

Both $p\left(x\right)$ and $q\left(x\right)$ are always continuous.

So, $p\left(q\right(x\left)\right)$ is always continuous

So, $\sin \left(x^2\right)$ is a continuous function.