Erify that g is the inverse on the one-to-one function f by showing that g[f( x )] = x and f[g( x )] = x. ?

Question

Verify that g is the inverse on the one-to-one function f by showing that g[f( x )] = x and f[g( x )] = x. Sketch the graphs of f, g, and the line y=x in the same coordinate system.

f(x) = √x+2; g(x) = x^2 +2 , x ≥0

Ps. x+2 are both under the square root

Graphing f, g, and the line y = x in a square root viewing window on a graphing utility?

Answer 1

You have a typo or you copied the question incorrectly:

Either f(x) = √(x-2) or g(x) = x^2 - 2.

Answer 2

You want to graph those two functions.  However, be careful of wording in textbooks.  I know that usually when they say "sketch" you should not be using a graphing calculator.  Those are also easy functions to sketch anyways.  By saying "graph the equations" you are allowed to use a graphing calculator.  To show that these two functions are inverse, they should reflect eachother opposite the y=x line.