Question

Find the inverse of the function f(x) = 5/6x +10

Answer 1

`\displaystyle f^(-1)(x)=(6x-60)/(5)`

Explanation:

Inverse function

Given the function

`\displaystyle f(x)=(5)/(6)x+10`

We find its inverse following the procedure below:

• Set y=f(x)

`\displaystyle y=(5)/(6)x+10`

• Multiply by 6:

`6y=5x+60`

• Operate:

`5x=6y-60`

• Solve for x:

`\displaystyle x=(6y-60)/(5)`

• Swap variables:

`\displaystyle y=(6x-60)/(5)`

• Make the new y the inverse function:

`\boxed{\displaystyle f^(-1)(x)=(6x-60)/(5)}`

This is the inverse function