Show that the function defined by `f(x)=cos(x^2)`is a continuous function.

Explanation

Let h(x) = `x ^(2) and g(x) = cos x`
h (x) =` x^(2)` is a polynimial function which is continuous for all real value of x and g(x) = cos x is
continuous for all real value of x.
Now `(goh ) (x) = g[ h(x)]`
=g `(x^(2)) = cos x ^(2)`
`:'` g(x) and h(x) are both continuous functions.
`:.` Composite function (goh) (x) is also continuous function.
`rArr cos x^(2)` is contnuous for all x `in` R. `" "`Hence proved.