Question

F(x)= 1/x−3+7 Find the inverse of f(x) and its domain.

Answer 1

C.

`f^(-1)(x)=(1)/(x-7)+3,\text{ where x }\\e7`

Step-by-step explanation:

Given the below function;

`f(x)=(1)/(x-3)+7`

To find the inverse of the above function, we have to follow the below steps;

1. Replace f(x) with y;

`y=(1)/(x-3)+7`

2. Switch x and y;

`x=(1)/(y-3)+7`

3. Solve for y;

`\begin{gathered} x-7=(1)/(y-3) \\ (y-3)(x-7)=1 \\ y-3=(1)/(x-7) \\ y=(1)/(x-7)+3 \end{gathered}`

4. Replace y with f^-1 (x);

`f^(-1)(x)=(1)/(x-7)+3`

To find the domain of the function, we need to consider that value of x that will make the function undefined and exclude it. That value of x is 7. So x must not be equal to 7.

Therefore, the solution is as written below;

`f^(-1)(x)=(1)/(x-7)+3,\text{ where x }\\e7`