inversa de $$ g(x)=\sqrt{2-x} $$

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La función inversa de $$ g(x)=\sqrt{2-x} $$ es $$ g^{-1}(x) = -x^{2}+2 $$. Find the inverse of the function $$ g(x)=\sqrt{2-x} $$ Function by following steps: - step0: Find the inverse: $$g\left(x\right)=\sqrt{2-x}$$ - step1: Replace $$g\left(x\right)$$ with $$y:$$ $$y=\sqrt{2-x}$$ - step2: Interchange the variables: $$x=\sqrt{2-y}$$ - step3: Swap the sides: $$\sqrt{2-y}=x$$ - step4: Raise both sides to the $$2$$-th power$$:$$ $$\left(\sqrt{2-y}\right)^{2}=x^{2}$$ - step5: Evaluate the power: $$2-y=x^{2}$$ - step6: Move the constant to the right side: $$-y=x^{2}-2$$ - step7: Change the signs: $$y=-x^{2}+2$$ - step8: Replace $$y$$ with $$g^{-1}\left(x\right):$$ $$g^{-1}\left(x\right) = -x^{2}+2$$ La función inversa de $$ g(x)=\sqrt{2-x} $$ es $$ g^{-1}(x) = -x^{2}+2 $$.

inversa de \( g(x)=\sqrt{2-x} \)

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inversa de \( g(x)=\sqrt{2-x} \)

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