Question

I really need help!!!

Answer 1

The inverse is:
`\sf f^(-1)(x) = 2-(4)/(x)`

The domain of the inverse function is all real numbers except for 2.

Domain restriction: x ≠ 2.

Explanation:

To find the inverse of
`\sf f(x) = (4)/(2-x)`, we can swap the x and y variables and solve the resulting equation for y.

`\sf y = (4)/(2-x)`

Swap the value of x and y.

`\sf x = (4)/(2-y)`

Doing Criss cross Multiplication:

`\sf 2-y= (4)/(x)`

Isolate y.

`\sf 2-(4)/(x) = y`

`\sf y= 2-(4)/(x)`

Therefore, the inverse of f(x) is the function is:

`\sf f^(-1)(x) = 2-(4)/(x)`

Since the original function has a hole at x = 2, the inverse function will have an asymptote at x = 2.

Therefore, the domain of the inverse function is all real numbers except for 2.