Respuesta :

dalendrk
[tex]y=2x^2-4\ \ \ |add\ 4\ to\ both\ sides\\\\2x^2=y+4\ \ \ |divide\ both\ sides\ by\ 2\\\\x^2=\dfrac{y+4}{2}\\\\x=\sqrt{\dfrac{y+4}{2}}\\\\\boxed{f(x)=2x^2-4\to f^{-1}(x)=\sqrt{\frac{x+4}{2}}} [/tex]
adioabiola

The inverse of the function y = 2x^2 –4 is;. y = √(x +4)/2

To find the inverse of the function;

  • We must first solve for x in the equation as follows;

  • y = 2x² - 4

  • y + 4 = 2x²

  • x² = (y +4)/2

  • x = √ (y +4)/2

By swapping x and y; we then have;

  • y = √(x +4)/2

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