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

Question

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

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Answer

Let $f\left( x \right) = {x^2}$ and $g\left( x \right) = \cos x$, then

$\left( {gof} \right)\left( x \right) = g\left[ {f\left( x \right)} \right] = g\left( {{x^2}} \right) = \cos {x^2}$

Now f and g being continuous it follows that their composite (gof) is continuous.

Hence $\cos {x^2}$ is continuous function.

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