Vega Matthews
06/30/2023 · Elementary School
inversa de \( f(x)=2-x^{2} \)
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Step-by-step Solution
Para encontrar la inversa de la función \( f(x)=2-x^{2} \), primero necesitamos intercambiar las variables \( x \) e \( y \) y luego resolver la ecuación resultante para \( y \).
1. Intercambiamos las variables \( x \) e \( y \):
\[ x = 2 - y^{2} \]
2. Resolvemos la ecuación para \( y \):
\[ y^{2} = 2 - x \]
\[ y = \pm \sqrt{2 - x} \]
Por lo tanto, la inversa de la función \( f(x)=2-x^{2} \) es:
\[ f^{-1}(x) = \pm \sqrt{2 - x} \]
Quick Answer
La inversa de \( f(x)=2-x^{2} \) es \( f^{-1}(x) = \pm \sqrt{2 - x} \).
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