Functions and the Casio Calculator fog(x)

When finding fog(x) the CAS calculator does a good job of simplifying algebraic steps, often to the point of making traditional questions trivial in the calculator section.

I'll start by defining a function f(x) =2x+1 and g(x)=x^2 and attempting to find fof(x), fog(x) and the inverse of (fog(x)).

To define a function f(x) go to the Main window and select

Interactive->Define

A window will appear

Enter the function name (eg. f)
Variable (eg. x)
Expression (eg. 2x+1)

The main window will reply:
Define f(x)=2(x)+1
done

Repeat:

Interactive->Define
Enter the function name (eg. g)
Variable (eg. x)
Expression (eg. x^2)

The main window will reply:
Define g(x)=x^2
done


To find fof(x)

In the main window
Action->Transformation->simplify
f(f(x)) (using the soft keyboard)
press exe

The main window should say
simplify(f(f(x))
4x+3



To find fog(x)

In the main window
transformation->simplify
f(g(x)) (using the soft keyboard)
press exe

The main window should say
simplify(f(g(x))
2x^2+1



To find inverse of fog(x)

In the main window
action->transformation->simplify
action->assistant->invert
action->advanced->solve
y=f(g(x)),x))) (using the soft keyboard= don't forget the "y=")
press exe

The main window should say
simplify(invert(solve(y=f(g(x)),x)))

Here is a link to other CAS calculator posts.