Algebra/Trig Review - Pauls Online Math Notes - Lamar University

Algebra/Trig Review⎛ f ⎞⎜ ⎟⎝ g ⎠( x)==f( x)( )g xx − x+1−20x23 10(c)( fg )( x) = f ( x) g ( x)= ( 3x 2 − x+ 10)( 1−20x)=− + − +3 260x 23x 201x10(d) For this problems (and the next two) remember that the little circle , , in thisproblem signifies that we are doing composition NOT multiplication!The basic formula for composition is( f g)( x) = f ( g( x))In other words, you plug the second function listed into the first function listedthen evaluate as appropriate.In this case we’ve got a number instead of an x but it works in exactly the sameway.f g 5 = f g 5( )( ) ( ( ))= f ( −99)= 29512(e) Compare the results of this problem to (c)! Composition is NOT the same asmultiplication so be careful to not confuse the two!f g x = f g x( )( ) ( ( ))= f ( 1−20x)2( x) ( x)= 3 1−20 − 1− 20 + 102( )= 3 1− 40x+ 400x − 1+ 20x+1021200 100 12= x − x+(f) Compare the results of this to (e)! The order in which composition is written isimportant! Make sure you pay attention to the order.gf x = g f x( )( ) ( ( ))2( 3 10)2( x x )= g x − x+= 1−20 3 − + 10=− x + x−260 20 199© 2006 Paul Dawkins 15http://tutorial.math.lamar.edu/terms.aspx