The interval notation for the range of w(r(x)) is (-∞,0].
What is the range of a function?
The range of a function is the desired set of values(dependent variables) for which the function is defined.
From the given information:
r(x) = 2 - x² and;
w(x) = x - 2
The function of w(r(x)) is determined by replacing the value of x in w(x) with r(x).
So,
[tex]\mathbf{w(r(x)) = (2-x^2) -2 }[/tex]
w(r(x)) = -x²
The range of w(r(x)) = -x² is the values of f(x) for which f(x) ≤ 0. The interval notation for the range of w(r(x)) is (-∞,0].
Learn more about the range of a function here:
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