What is the inverse of f(x)=(x−5)^2 for x≥5 where function g is the inverse of function f?

g(x)=√x−5, x≥5

g(x)=√x+5, x≥−5

g(x)=√x −5, x≥0

g(x)=√x +5, x≥0

Question

What is the inverse of f(x)=(x−5)^2 for x≥5 where function g is the inverse of function f?

g(x)=√x−5, x≥5

g(x)=√x+5, x≥−5

g(x)=√x  −5, x≥0

g(x)=√x  +5, x≥0

AZ · Answer

To find the inverse of a function we have to switch the x and y and solve for y
So let's just change f(x) to y to make things simpler.

So, first let's switch x and y

y = (x-5)^2
x = (y - 5)^2

All you have to do is swap their places. Now you have to solve for y!

So first things first, how will we get rid of the  $ ^2$  on the right side?

We can take the square root of both sides! What do you get when that happens?