Math  /  Algebra

QuestionFind the domain and range of f(x)=3+2xf(x)=\sqrt{3+2x} and its inverse f1(x)f^{-1}(x).

Studdy Solution
The range of the inverse function f(x)f^{-}(x) is the domain of the original function f(x)f(x). So, the range of f(x)f^{-}(x) is {yy32}\{y \mid y \geq -\frac{3}{2}\}.
In conclusion, for the function f(x)=3+2xf(x)=\sqrt{3+2x}i) the domain is {xx32}\{x \mid x \geq -\frac{3}{2}\}, ii) the range is {yy}\{y \mid y \geq\}, iii) the domain of the inverse is {xx}\{x \mid x \geq\}, iv) the range of the inverse is {yy32}\{y \mid y \geq -\frac{3}{2}\}.

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