Question 1006762
Step 1) Replace f(x) with y
Step 2) Swap x and y
Step 3) Solve for y



{{{f(x)= -3x^3-5 }}}



{{{y= -3x^3-5 }}} Step 1)



{{{x= -3y^3-5 }}} Step 2)



Now we solve for y.



{{{x+5= -3y^3-5+5 }}} Add 5 to both sides



{{{x+5= -3y^3 }}} 



{{{-3y^3=x+5}}} 



{{{(-3y^3)/(-3)=(x+5)/(-3)}}} Divide both sides by -3



{{{y^3=-(x+5)/3}}} 



{{{root(3,y^3)=root(3,-(x+5)/3)}}} Apply the cube root to both sides



{{{y=root(3,-(x+5)/3)}}}



The inverse function is *[Tex \LARGE f^{-1}(x) = \sqrt[3]{-\frac{x+5}{3}}]