Find the inverse of
g(x) = 4x^3 + 5

Step-by-step explanation:

To find the inverse of a function, you can switch the "x" and "y" variables, then isolate "y", then change it back to function notation with the superscript ⁻¹.

You can't see "y" in the given function, but y = g(x). g(x) is the way you write "y" in function notation. The inverse function notation is g⁻¹(x).

  Change "g(x)" to "y"

  Switch the "x" and "y" variables

  Subtract 5 from both sides to start isolating "y"

  5 - 5 cancels out on right side

  Divide both sides by 4

  4y³/4 cancels out the 4 on the right side

  Cube root both sides

  ∛y³ cancels out the ³ on the right side

  Variable on left side is standard formatting

  Change the inverse function notation g⁻¹(x)

The inverse of g(x) = 4x³ + 5 is g⁻¹(x) = ∛[(x-5)/4].

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