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# Function

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If f(x) is a function whose domain is [-25,5] and g(x) = f(x^2), then the domain of g(x) is an interval of what width?

Oct 24, 2022

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All of the values of x from [-25, -sqrt 5) would get squared and turned positive, and outside of the domain. So they don't work.

All of the values of x from (sqrt 5, 5] would get squared outside of the domain of f(x). So they don't work.

Everything inside those still works, so the width of the interval is $$2\sqrt5$$.

Oct 24, 2022