Woojin L.
asked • 09/16/21If f(x)=x² on the domain[-2,2] then f⁻¹ is
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Raphael K. answered • 09/16/21
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I genuinely love teaching Calculus and have for 10+ years.
The trick here is that y=x^2 is a parabola. Thus, once converted into the inverse function of the form f-1(x) = +/- √(x) , we must chose either the positive or the negative square root function for the inverse, because with both, it is technically not a function, since it violates the vertical line test. Sneaky
Woojin L.
so it doesn't exist?
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09/16/21
Raphael K.
No, the domain does indeed exist. The domain of the inverse function is [0,4]
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09/16/21
Raphael K.
The range is limited from [0,2] and does not include the lower portion, or the negative square root function, because if it did, it would not be considered a function, as it violate the vertical line test.
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09/16/21
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Raphael K.
Oh the domain would be from [0,4] because the x's of the original function become the y's of the inverse function. As do the y's become the x's. Therefore, since the original function has a domain of [-2,2], the inverse function has a domain of [0,4] because, the domain for the inverse is simply the y's for the original function.09/16/21