find the inverse of g(x)=x³-2​

The inverse of g(x) = x³ - 2 is g⁻¹(x) = ∛x+2To find the inverse of the function, first we must write the function and replace g(x)  to y g(x) = x³ - 2y = x³-2Next, you must interchange the position of x and yx = y³-2Transpose 2x+2 = y³We need to make y³ into y so we get the cube root of both sides∛(x+2) =∛y³∛(x+2) =y³Use symmetric property (If a = b, then b = a)y³=∛(x+2)Change y to g⁻¹(x)g⁻¹(x)=∛(x+2)Therefore, the inverse of g(x) = x³-2 is [tex]$$ f^{-1}(x) = \sqrt[3]{x + 2} $$[/tex]

Answered by keinasour | 2025-07-29

[tex]\boxed{g^{-1}(x) = \sqrt[3]{x + 2}}[/tex]

Answered by ykrio | 2025-07-29