Find a Symbolic Representation for F^-1(x)

Question

Find a Symbolic Representation for F^-1(x)    

 

F(x) = ^3√¯10x

 

f^-1(x) =?

Answer 1

y = f(x) = (10x)^(1/3)

 

Invert variables:

 

x = (10y)^(1/3)

 

cube both sides

 

x^3 = 10y

 

divide both sides by 10

 

(x^3)/10 = y

 

y = f^-1(x) = (x^3)/10