If f(x) = 5-2x^3, what is f^-1(x)?

1 Answer
Feb 24, 2018

f^-1(x)=root(3)(-1/2(x-5))

Explanation:

f(x)=y

y=5-2x^3

Switch the places of x and y:

x=5-2y^3

Now, solve for y:

x-5=-2y^3

y^3=-1/2(x-5)

Take the cube root of both sides:

root(3)y=root(3)(-1/2(x-5))

y=root(3)(-1/2(x-5))

Now that we have solved for y after switching the places of x and y, y=f^-1(x)

f^-1(x)=root(3)(-1/2(x-5))