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

Which function is the inverse of Ax) =-x?- 97OA. (-40) = 95 + 9OB. (-HI) = V-=9OC-example-1
User Bamerza
by
3.2k points

1 Answer

8 votes
8 votes

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.

User Louis Jacomet
by
2.4k points
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