Answer
a) $(f\circ g)(2)=-26$
b) $(g\circ f)(-2)= -241$
c) $(f\circ f)(4)= 16$
d) $(g\circ g)(-1)=-1$
Work Step by Step
a) $(f\circ g)(x)= f(g(x))=3(1-2x^2)-5$
$f(g(2))=3(1-2(2)^2)-5=3(1-8)-5=3(-7)-5=-21-5=-26$
b) $(g\circ f)(x)= g(f(x))=1-2(3x-5)^2$
$g(f(-2))=1-2(3(-2)-5)^2=1-2(-11)^2=1-2(121)=1-242=-241$
c) $(f\circ f)(x)= f(f(x))=3(3x-5)-5$
$f(f(4))=3(3(4)-5)-5=3(7)-5=21-5=16$
d) $(g\circ g)(x)= g(g(x))=1-2(1-2x^2)^2$
$g(g(-1))=1-2(1-2(-1)^2)^2=1-2(1-2)^2=1-2(1)=-1$
