Question

Find the inverse function of

f(x)= (2-x^3)^5

Answer 1

@Coolsector f(x)^(1/5) = 2-x^3 ---> x^3 = 2- f(x)^(1/5)
:)

Answer 2

oops! you are right

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

ill call f-1(x) the inverse of f(x) so :

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

Answer 3

im confused after -f(x)^(1/5)+2=x^3

Answer 4

where?

Answer 5

what is my next step

Answer 6

1. first you want to switch x and y (and since f(x) can also be written as y)
for example:
y = (2-x^3)^5 (eqn. 1) will become
x = (2-y^3)^5 (eqn. 2)
Then you want to isolate y from eqn. 2. using algebra

Answer 7

take the 5th root of both sides

Answer 8

Yes.. so then you'll have \[\sqrt[5]{x} = (2-y ^{3})\] so what will you do?