Question

what is the inverse of the function f(x) = 4x^3 - 9

Answer 1

Answer:

$f(x)^-^1=\sqrt[3]{\frac{x+9}{4}}$

Step-by-step explanation:

Finding the inverse of a function is essentially doing a given function in backwards order. An easy trick to doing such is to treat the evaluation (f(x)) like a variable. Think of the function as an equation, then solve the function for (x) in terms of (f(x)).

$f(x)=4x^3-9$

Inverse operations,

$f(x)=4x^3-9\\\\(f(x))+9=4x^3\\\\\frac{((f(x))+9)}{4}=x^3\\\\\sqrt[3]{\frac{(f(x))+9}{4}}=x$

Now put this in the form of an inverse function, switch the places of the terms (x) and (f(x)), remember to indicate that it is an inverse function,

$f(x)^-^1=\sqrt[3]{\frac{x+9}{4}}$