# How do you write #y = 1/(x^2 + 3)# as a composition of two simpler functions?

You can write ( y = \frac{1}{x^2 + 3} ) as the composition of two simpler functions as follows:

Let ( u(x) = x^2 + 3 ) and ( v(u) = \frac{1}{u} ). Then, ( y = v(u(x)) ).

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Refer to explanation

You can write it as a composition of the following functions

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You can write ( y = \frac{1}{x^2 + 3} ) as a composition of two simpler functions by decomposing the denominator into its factors. In this case, ( x^2 + 3 ) can be factored as ( (x + \sqrt{3}i)(x - \sqrt{3}i) ), where ( i ) is the imaginary unit. Thus, you can rewrite ( y ) as ( y = \frac{1}{(x + \sqrt{3}i)(x - \sqrt{3}i)} ). Then, you can express ( y ) as a composition of two simpler functions, ( f(x) = \frac{1}{x + \sqrt{3}i} ) and ( g(x) = \frac{1}{x - \sqrt{3}i} ). Therefore, ( y = f(g(x)) ).

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