select the correct answer. which function is the inverse of $f(x)=-x^{3}-9$?\na. $f^{-1}(x)=sqrt3{x +…

select the correct answer. which function is the inverse of $f(x)=-x^{3}-9$?\na. $f^{-1}(x)=sqrt3{x + 9}$\nb. $f^{-1}(x)=sqrt3{-x - 9}$\nc. $f^{-1}(x)=-sqrt3{-x + 9}$\nd. $f^{-1}(x)=-sqrt3{x - 9}$

select the correct answer. which function is the inverse of $f(x)=-x^{3}-9$?\na. $f^{-1}(x)=sqrt3{x + 9}$\nb. $f^{-1}(x)=sqrt3{-x - 9}$\nc. $f^{-1}(x)=-sqrt3{-x + 9}$\nd. $f^{-1}(x)=-sqrt3{x - 9}$

Answer

Explanation:

Step1: Let $y = f(x)$

$y=-x^{3}-9$

Step2: Swap $x$ and $y$

$x = -y^{3}-9$

Step3: Solve for $y$

First, add 9 to both sides: $x + 9=-y^{3}$. Then multiply both sides by - 1: $-x - 9=y^{3}$. Take the cube - root of both sides: $y=\sqrt[3]{-x - 9}$. So $f^{-1}(x)=\sqrt[3]{-x - 9}$.

Answer:

B. $f^{-1}(x)=\sqrt[3]{-x - 9}$