> #mathematics , #functions , #domain , #in-mathematic-grade-11 > The domain of f(x) =x^2 sgnx is???
Anonymous
Oct 28, 2023

The domain of f(x) =x^2 sgnx is???

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Oct 28, 2023
The domain of a function is the set of all possible input values for which the function is defined.

In this case, the function is f(x) = x^2 sgn(x), where sgn(x) is the sign function. The sign function returns -1 if x is negative, 0 if x is zero, and 1 if x is positive.

Since x^2 is defined for all real numbers, the only restriction on the domain comes from the sign function. The sign function is defined for all real numbers except for x = 0, where it is undefined.

Therefore, the domain of f(x) = x^2 sgn(x) is all real numbers except for x = 0. In interval notation, the domain can be written as (-∞, 0) U (0, ∞).
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