Question

Which of the following is the inverse of the given function? Y=3x^5-4

Answer 1

`y\textrm{ }=\textrm{ }(\frac{x\textrm{ }+\textrm{ }4}{3} )^{(1)/(5) }`

Explanation:

Given function
`y\textrm{ }=\textrm{ }3x^(5)\textrm{ }-\textrm{ }4`

To find an inverse for any given function, which is of the form
`y=f(x)`, always swap
`x` and
`y` in the equation and try to get the form
`x=f(y)`. Now, swapping back
`x` and
`y`, we get the inverse function.

On swapping
`x` and
`y`, we get
`x\textrm{ }=\textrm{ }3y^(5)\textrm{ }-\textrm{ }4`

`y\textrm{ }+\textrm{ }4\textrm{ }=\textrm{ }3x^(5)`

`x^(5)\textrm{ }=\textrm{ }\frac{y\textrm{ }+\textrm{ }4}{3}`

`x\textrm{ }=\textrm{ }(\frac{y\textrm{ }+\textrm{ }4}{3} )^{(1)/(5) }`

Swapping back
`x` and
`y`, we get
`y\textrm{ }=\textrm{ }(\frac{x\textrm{ }+\textrm{ }4}{3} )^{(1)/(5) }`

This is the inverse function.