Look at image attached

How do you do the inverse of this function?

9514 1404 393

  f^-1(x) = <see attachment>

Step-by-step explanation:

If we write the function as ...

  f(x) = ∛x +101/128x

Then the inverse function is the value of y when ...

  x = f(y)

This resolves to a cubic in y, whose solution can be found by use of any of the various cubic solution formulas. You can find the cubic by ...

  x = ∛y +by . . . . . . where b = 101/128

  x -by = ∛y . . . . . . . subtract by

  (x -by)³= y . . . . . . cube both sides

If we subtract the left side and expand the cube, we get ...

  b³y³ -3b²xy² +(1 +3bx²)y -x³ = 0 . . . . . . . a cubic in y

There will be one real and two complex solutions to this cubic. The real solution can be written in the form shown in the attachment. That is, ...

  y = f⁻¹(x) = [attachment expression]

A graph of it is shown in the second attachment. It is the reflection of f(x) across the line y = x, as an inverse function should be.

_____

Additional comment

The idea here is to show that it is possible to write an expression for the inverse function. It is not pretty, and it is somewhat tedious to evaluate.

29 is the correct answer

step-by-step explanation:

answer: bea's uncle is 25 years old.

step-by-step explanation:

given the equation , we can say that the variable "x" represents the age of bea's uncle. then to find his age, we need to solve for "x":

we must add 15 to both sides of the equation:

now we need to divide both sides of the equation by 3:

therefore, we can conclude that bea's uncle is 25 years old.