Question

For the funtion f(x)= (x+7)^5, Find f^-1 (x)

a: f^{-1}(x)=\sqrt[5]{x}+7f −1(x)=5x +7
b: f^−1(x)=x 5 −7
c: f −1(x)=5sqrtx−7
d: f ^−1(x)= 5sqrtx​−7

Answer 1

The inverse of function
`f(x)= (x+7)^5` is
`\mathbf{f^(-1) (x)=\sqrt[5]{x}+7}`

Option A is correct option.

Explanation:

For the function
`f(x)= (x+7)^5`, Find
`f^(-1) (x)`

For finding inverse of x,

First let:

`y=(x+7)^5`

Now replace x with y and y with x

`x=(y+7)^5`

Now, solve for y

Taking 5th square root on both sides

`\sqrt[5]{x}=\sqrt[5]{(y+7)^5}\\\sqrt[5]{x}=y+7\\=> y+7=\sqrt[5]{x}\\y=\sqrt[5]{x}-7`

Now, replace y with
`f^(-1) (x)`

`f^(-1) (x)=\sqrt[5]{x}+7`

So, the inverse of function
`f(x)= (x+7)^5` is
`\mathbf{f^(-1) (x)=\sqrt[5]{x}+7}`

Option A is correct option.