Answer: [tex]a)\quad f^{-1}(x)=\sqrt[3]{\dfrac{x+5}{3}}[/tex]
Step-by-step explanation:
Inverse is when you swap the x's and y's and solve for y. Note: f(x) is y
[tex]y=3x^3-5\\\\\text{Swap the x's and y's:}\\x=3y^3-5\\\\\text{Add 5 to both sides:}\\x+5=3y^3\\\\\text{Divide both sides by 3:}\\\dfrac{x+5}{3}=y^3\\\\\\\text{Take cubed root of both sides:}\\\sqrt[3]{\dfrac{x+5}{3}}=y[/tex]
