Answer
a) 97; b) -81.5; c) 1; d) -1.5.
Work Step by Step
We are given the functions:
$f(x)=4x^2-3$
$g(x)=3-\dfrac{1}{2}x^2$
a) $(f\circ g)(4)=f(g(4))=f\left(3-\dfrac{1}{2}\cdot 4^2\right)=f(-5)=4(-5)^2-3=97$
b) $(g\circ f)(2)=g(f(2))=g(4(2^2)-3)=g(13)=3-\dfrac{1}{2}(13^2)=-81.5$
c) $(f\circ f)(1)=f(f(1))=f(4(1^2)-3)=f(1)=4(1^2)-3=1$
d) $(g\circ g)(0)=g(g(0))=g\left(3-\dfrac{1}{2}(0^2)\right)=g(3)=3-\dfrac{1}{2}(3^2)=-1.5$
