1 DODATNI ZADACI ZA VEŽBANJE -Funkcije- 1. Neka su :f → \ \ i : g ...

1. Neka su f :DODATNI ZADACI ZA VEŽBANJE-Funkcije-→ i g : → realne funkcije. Odrediti: a) f g b) gf1) f ( x) = x+ 2 , g( x) = 3x−43x+ 4 7x−1=72f x =2x , g( x) = 4x− 1f x = 8x, g( x) =− 2x+1f x5x−1−4x− 3= , g( x)=272) f ( x)= , g( x)3) ( ) 524) ( )5) ( )Rešenje:1) f ( x) = x+ 2 , g( x) = 3x−4a) ( )( ) ( ( )) ( ) ( )f g x = f g x = f 3x− 4 = 3x− 4 + 2= 3x− 4+ 2= 3x−2b) ( )( ) ( ( )) ( ) ( )g f x = g f x = g x+ 2 = 3 x+ 2 − 4= 3x+ 6− 4= 3x+23x+ 472) f ( x)= , g( x)a) ( )( ) ( ( ))7x−1=2⎛7x −1⎞ 3 421x−3 21x− 3+ 8 21x+547x1⎜ ⎟2 + +⎛ − ⎞ 2 2 2 21x+5f g x = f g x = f⎝ ⎠⎜ ⎟= = = = =⎝ 2 ⎠ 7 7 7 7 14⎛3x+ 4⎞ 7 13x 4⎜ ⎟ −⎛ + ⎞ 7 3x+ 4−1 3x−3g f x = g f x = g⎝ ⎠⎜ ⎟= = =⎝ 7 ⎠ 2 2 2b) ( )( ) ( ( ))23) f ( x) = 5x, g( x) xa) ( )( ) ( )= 4 − 1( ) ( ) ( )f g x = f g x = f x − = x − = x −b) ( )( ) ( )2 2 24 1 5 4 1 20 5( ) ( ) ( ) 2 2 2g f x = g f x = g 5x = 4 5x − 1= 4⋅25x − 1= 100x−124) f ( x) = 8x, g( x) =− 2x+1a) ( )( ) ( )( ) ( ) ( ) ( )2 2 2f g x = f g x = f − 2x+ 1 = 8 − 2x+ 1 = 8 4x − 4x+ 1 = 32x − 32x+8b) ( )( ) ( )( ) ( ) ( )g f x = g f x = g x =− x + =− x +5) f ( x)= , g( x)a) ( )( ) ( ( ))2 2 28 2 8 1 16 15x−1−4x−3=27⎛−4x −3⎞ 5 1−20x−15 −7 −20x−224x 3⎜ ⎟⎛− − ⎞ 7 −7 7 −20x−22 −10x−11f g x = f g x = f⎝ ⎠⎜ ⎟= = = = =⎝ 7 ⎠ 2 2 2 14 7⎛5x−1⎞ −4 3− 20x+ 4 −65x 1⎜ ⎟−⎛ − ⎞ 2 2 −20x−2 −10x−1g f x = g f x = g⎝ ⎠⎜ ⎟= = = =⎝ 2 ⎠ 7 7 14 7b) ( )( ) ( ( ))1