Let f:R→R  and g:R→R  be two real-valued functions.  Let S  be the solution set of the equation f(x)=g(x) , and let T  be the solution set of the modified equation (f(x))^2=(g(x))^2 .  Show that SS  is a subset of T , but that S  and T  are not necessarily equal

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ISBN:9780470458365
Author:Erwin Kreyszig
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Let f:R→R  and g:R→R  be two real-valued functions.  Let S  be the solution set of the equation f(x)=g(x) , and let T  be the solution set of the modified equation (f(x))^2=(g(x))^2 .  Show that SS  is a subset of T , but that S  and T  are not necessarily equal.

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