Question

Determine the inverse of the function f(x)=|x-5| for x (greater than or equal to) 5. Then complete the inequality for the domain restrictions of the inverse function
F^-1(x)=______
The domain restriction of f^-1(x) is x (greater than or equal to)

Answer 1

Answer:

$f^{-1}(x)=x+5.$

The domain of the function $f^{-1}(x)$ is $x\ge 0$ (greater than or equal to 0).

Step-by-step explanation:

If $x\ge 5,$ then the expression $x-5$ takes values that are greater or equal than 0. Thus,

$f(x)=|x-5|=x-5\text{ for }x\ge 5.$

To find the inverse function you have to express x in terms of y and then change x into y and y into x:

$y=x-5,\\ \\x=y+5$

and

$f^{-1}(x)=x+5.$

The domain of the function $f(x)$ is $x\ge 5$ and the range of the function $f(x)$ is $y\ge 0.$ The domain of the inverse function $f^{-1}(x)$ is the range of the function $f(x),$ hence the domain of the function $f^{-1}(x)$ is $x\ge 0.$