Answer
(a) $97$
(b) $-\dfrac{163}{2}$
(c) $1$
(d) $-\dfrac{3}{2}$
Work Step by Step
a) $(f\circ g)(4)= f(g(4))=f(3-\frac{1}{2}\times4^{2})=f(-5)=4(-5)^{2}-3=97$
b) $(g\circ f)(2)=g(f(2))=g(4\times2^{2}-3)=g(13)=3-\frac{1}{2}\times13^{2}=-\dfrac{163}{2}$
c) $(f\circ f)(1)=f(f(1))=f(4\times1^{2}-3)=f(1)=4\times1^{2}-3=1$
d) $(g\circ g)(0)=g(g(0))=g(3-\frac{1}{2}\times0^{2})=g(3)=3-\frac{1}{2}\times3^{2}=-\dfrac{3}{2}$
