Question

If f(x) = 5-2x^3 and f^-1 denotes the inverse function of f, then f^-1(x)= ?

Please show all of your work! Thank-you!

Answer 1

$f(x)=5-2x^3\\ y=5-2x^3\\ 2x^3=-y+5\\ x^3=-\dfrac{y-5}{2}\\ x=\sqrt[3]{-\dfrac{y-5}{2}}=-\sqrt[3]{\dfrac{y-5}{2}}\\ f^{-1}(x)=-\sqrt[3]{\dfrac{x-5}{2}}$