Question

Determine the inverse of the followingy =- log(x - 1) + 2

Answer 1

Step 1:

Write the function

`\text{y = - }\log ^((x-1))_{}\text{ + 2}`

Step 2:

To find the inverse of the function, make x subject of the formula

`\begin{gathered} y\text{ = - }\log ^((x-1))_{}+\text{ 2} \\ \log ^((x-1))_{}\text{ = 2 - y} \\ x-1\text{ = }10^((2-y)) \\ x=10^((2-y))\text{ + 1} \\ y^(-1)(x)=10^((2-x))\text{ + 1} \end{gathered}`
`\begin{gathered} Or \\ y^(-1)(x)\text{ = ln(2-x) + 1} \end{gathered}`