Question

If f(x) = 3x^4 + 5, find the inverse of f.

Answer 1

`f\placeholder{⬚}^(-1)(x)\text{ = \lparen}(x-5)/(3))\placeholder{⬚}^{(1)/(4)}`

Step-by-step explanation:

Here, we want to find the inverse of the given function

We proceed as follows:

`\begin{gathered} we\text{ set:} \\ y\text{ = 3x}^4+5 \\ y-5\text{ = 3x}^4 \\ x^4\text{ = }(y-5)/(3) \\ \\ x^\text{ = }\sqrt[4]{(y-5)/(3)} \\ \\ x\text{ = \lparen}(y-5)/(3))\placeholder{⬚}^{(1)/(4)} \end{gathered}`

Now, we switch x and y:

`f\placeholder{⬚}^(-1)(x)\text{ = \lparen}(x-5)/(3))\placeholder{⬚}^{(1)/(4)}`