How to solve according to the given directions?

Question

f(x)= ³√4x-7

A. name two conditions for existence of f^-1(x)

B. Find the inverse of f(x)


Thanks.

Answer 1

f(x) = ³√4x-7

y= ³√4x-7

x= ³√4y-7

³√4y= x+7

y= (x+7)/(³√4)

f^-1(x) = (x+7)/(³√4)

 

For a function to have an inverse then any horizontal line can only intersect the graph of said function at one and only one point

 

For a function f^-1(x) to be the inverse of f(x) then:

f(f^-1(x))=x    and    f^-1(f(x))=x