Show that the function defined by f(x) = (x^2) is a continuous fu… - Vidyadip

Question

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

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Answer

Observe that the function is defined for every real number.
The function $f$ may be thought of as a composition $g o h$ of the two functions $g$ and $h,$ where $g (x) = \sin x$ and $h (x) = x^2$.
Since both $g$ and $h$ are continuous functions,
Suppose $f$ and $g$ are real valued functions such that $(f o g)$ is defined at $c$. If g is continuous at $c$ and if $f$ is continuous at $g (c),$ then $(f o g)$ is continuous at $c$.

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