Show that the function defined by f(x) = sin (x2) is a continuous… - Vidyadip

Question

Show that the function defined by f(x) = sin (x²) 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) = x². 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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