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Jika f ( x ) = 1 − x 2 dan g ( x ) = 2 x + 1 , tentukan: a. f ( f ( x ) ) b. g ( g ( x ) ) c. f ( g ( x ) ) d. g ( f ( x ) )

Jika dan , tentukan:

a.

b.

c.

d.

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a. b. c. d.

a. begin mathsize 14px style f open parentheses f open parentheses x close parentheses close parentheses end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis f open parentheses x close parentheses right parenthesis end cell equals cell f open parentheses 1 minus x squared close parentheses end cell row cell f left parenthesis f open parentheses x close parentheses right parenthesis end cell equals cell 1 minus open parentheses 1 minus x squared close parentheses squared end cell row cell f left parenthesis f open parentheses x close parentheses right parenthesis end cell equals cell 1 minus open parentheses 1 minus 2 x squared plus x to the power of 4 close parentheses end cell row cell f left parenthesis f open parentheses x close parentheses right parenthesis end cell equals cell 1 minus 1 plus 2 x squared minus x to the power of 4 end cell row cell f left parenthesis f open parentheses x close parentheses right parenthesis end cell equals cell negative x to the power of 4 plus 2 x squared end cell end table end style

b. begin mathsize 14px style g open parentheses g open parentheses x close parentheses close parentheses end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis g open parentheses x close parentheses right parenthesis end cell equals cell g open parentheses 2 x plus 1 close parentheses end cell row cell g left parenthesis g open parentheses x close parentheses right parenthesis end cell equals cell 2 open parentheses 2 x plus 1 close parentheses plus 1 end cell row cell g left parenthesis g open parentheses x close parentheses right parenthesis end cell equals cell 4 x plus 2 plus 1 end cell row cell g left parenthesis g open parentheses x close parentheses right parenthesis end cell equals cell 4 x plus 3 end cell end table end style

c. begin mathsize 14px style f open parentheses g open parentheses x close parentheses close parentheses end style

begin mathsize 14px style f left parenthesis g open parentheses x close parentheses right parenthesis equals f open parentheses 2 x plus 1 close parentheses f left parenthesis g open parentheses x close parentheses right parenthesis equals 1 minus open parentheses 2 x plus 1 close parentheses squared f left parenthesis g open parentheses x close parentheses right parenthesis equals 1 minus open parentheses 4 x squared plus 4 x plus 1 close parentheses f left parenthesis g open parentheses x close parentheses right parenthesis equals 1 minus 4 x squared minus 4 x minus 1 f left parenthesis g open parentheses x close parentheses right parenthesis equals negative 4 x squared minus 4 x end style

d. begin mathsize 14px style g open parentheses f open parentheses x close parentheses close parentheses end style

begin mathsize 14px style g left parenthesis f open parentheses x close parentheses right parenthesis equals g open parentheses 1 minus x squared close parentheses g left parenthesis f open parentheses x close parentheses right parenthesis equals 2 open parentheses 1 minus x squared close parentheses plus 1 g left parenthesis f open parentheses x close parentheses right parenthesis equals 2 minus 2 x squared plus 1 g left parenthesis f open parentheses x close parentheses right parenthesis equals 3 minus 2 x squared end style

 

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Fungsi f dan g saling invers apabila f ∘ g = g ∘ f = I dengan I adalah fungsi identitas I ( x ) = x . Dalam hal ini dilambangkan g = f − 1 , yaitu merupakan fungsi invers dari .Misalkan f ( x ) = c x ...

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