SOLUTION: Can someone show me how to do a problem like this? This is a one to one function f(x)=sqare root of x-3. List the domain and range of the functin and its inverse in internal not

Question 169150: Can someone show me how to do a problem like this?
This is a one to one function f(x)=sqare root of x-3. List the domain and range of the functin and its inverse in internal notation.
Show that f of f^-1(x)=x
f^-1 of f= x
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Remember, the domain of the inverse function is simply the range of the original function. Since the range of the original function is , the domain of the inverse function is

Likewise, the range of the inverse function is the domain of the original function. Since the domain of the original function is , this means that the range of the inverse function is

If those two previous statements made no sense whatsoever, then just keep in mind that the domain and range switch when it comes to the inverse function.

Finding the inverse:

Start with the given function

Replace f(x) with y

Switch x and y. The goal now is to solve for y

Square both sides

Add 3 to both sides.

So the answer is which means that the inverse function is

with the restriction

"Show that f of f^-1(x)=x"

Start with the given function

Plug in

. In other words, replace each "x" in f(x) with

Combine like terms.

Take the square root of to get x

-----------------

"Show that f^-1 of f(x)=x"

Start with the inverse function

Plug in

Square to get

Combine like terms.
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