Question

What is the inverse of f(x)=(x-5)^2 for x greater or equal to 5 where function g is the inverse of function f

Answer 1

Answer:

$y=\sqrt{x}+5$

Step-by-step explanation:

The inverse of a function, is the function or rule formed by reflecting the line over y=x. This means essentially that all (x,y) values from the original function switch to (y,x).

(x,y)--->(y,x) in the new function.

If the function has points (-3,4) and (5,-2) then the inverse has points (4,-3) and (-2, 5).

We can find the equation of the inverse by switching x and y in the equation and solving for y.

This means that $y=(x-5)^2$ becomes $x=(y-5)^2$. We now solve for y through inverse operations.

$x=(y-5)^2$

$x=(y-5)^2\\\sqrt{x} =\sqrt{(y-5)^2} \\\sqrt{x} =y-5\\\sqrt{x} +5=y$