Question

Which function is the inverse of Ax) =-x?- 97OA. (-40) = 95 + 9OB. (-HI) = V-=9OC.BEI9OD.f-1x) =9

Answer 1

`f(x)=-x^3-9`

To find the inverse of f(x):

1. Substitute the f(x) by y:

`y=-x^3-9`

2. Solve x:

Add 9 in both sides of the equation:

`\begin{gathered} y+9=-x^3-9+9 \\ y+9=-x^3 \end{gathered}`

Multiply both sides of the equation by -1:

`\begin{gathered} -1(y+9)=-1(-x^3) \\ -y-9=x^3 \end{gathered}`

Take cubic root in both sides of the equation:

`\begin{gathered} \sqrt[3]{-y-9}=\sqrt[3]{x^3} \\ \\ x=\sqrt[3]{-y-9} \end{gathered}`

3.Change the y by x, and the x by f^-1 (x):

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

Then, the inverse of f(x) is B.