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.

Does the inverse give f(x), or g(x)?

ReplyDeleteIf I've done it correctly it should give the inverse of f(g(x))!!

ReplyDelete