Composing Functions

Shows how to check that the answer is the composition of two functions.

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Complete Code

Download file: ComposingFunctions.pg

POD for Macro Files

PG problem file

Explanation

DOCUMENT();
loadMacros('PGstandard.pl', 'PGML.pl', 'answerComposition.pl', 'PGcourse.pl');

Preamble

We need to include the macros file answerComposition.pl

Context()->variables->are(x => 'Real', y => 'Real', u => 'Real');

$a = random(2, 9);

$f = Formula("sqrt(u)");
$g = Formula("x^2+$a");

Setup

This perl code sets up the problem. 
BEGIN_PGML
Express the function [`y = \sqrt{x^2 + [$a]}`] as a composition [`y = f(g(x))`]
of two simpler functions [`y = f(u)`] and [`u = g(x)`].

    [`f(u) =`] [___]

    [`g(x) =`] [___]
END_PGML

Statement

This is the problem statement in PGML. 
COMPOSITION_ANS($f, $g);

Answer

This must be called with the method COMPOSITION_ANS with the arguments that will test for f(g(x))

BEGIN_PGML_SOLUTION
Solution explanation goes here.
END_PGML_SOLUTION

ENDDOCUMENT();

Solution

A solution should be provided here.