Question

The function defined by $f\left(x\right)=\sin \left(x^2\right)$ is a continuous function over R.If true enter 1 else 0.

Answer 1

$f\left(x\right)=\sin \left(x^2\right)\to 1$

Let $x^2=y\to 2$

$f\left(x\right)$ is composition of $\sin \left(y\right)=g\left(x\right)$ (say) and $y=x^2$ where $\sin \left(y\right)=g\left(x\right)$ is continuous over R and $y=x^2$ is also continuous in $xϵR$, we know that composition of two continuous functions is continuous, hence $f\left(x\right)$ is also continuous over R.