Question

Sendo f e g funções de domínio real com f(x)= x²+ 2x e g(x)= 3x, determine:

a) ( f °g )(x)

b) ( g ° f )(x)

Dadas as funções f(x)= 2x+1 e g(x)=2x+9, calcule:

a) f (g(2) )
  

b)g ( f(-3) ) 

Answer 1

1 )
a )

$(f\circ~g)(x)=f(g(x))\\ \\(f\circ~g)(x)=f(3x)\\ \\(f\circ~g)(x)=9x^2+6x$

b )

$(g\circ~f)(x)=g(f(x))\\ \\(g\circ~f)(x)=g(x^2+2x) \\(g\circ~f)(x)=3x^2+6x$

2 )

a )

$f(g(2))$

$g(2)=2.2+9\\g(2)=13$

$f(13)=2x+1\\f(g(2))=2.13+1\\f(g(2))=27$

b)

$g(f(-3))$

$f(-3)=2x+1\\f(-3)=2.(-3)+1\\f(-3)=-5$

$g(-5)=2x+9\\ \\g(f(-3))=2x+9 \\g(f(-3))=2.(-5)+9 \\g(f(-3))=-10+9 \\g(f(-3))=-1$