Answer
a. $x^4-4x^2+6$
b. $x^4+4x^2+2$
c. $6$
d. $34$
Work Step by Step
Given $f(x)=x^2+2$ and $g(x)=x^2-2$, we have:
a. $(f\circ g)(x)=(x^2-2)^2+2=x^4-4x^2+6$
b. $(g\circ f)(x)=(x^2+2)^2-2=x^4+4x^2+2$
c. $(f\circ g)(2)=(2)^4-4(2)^2+6=6$
d. $(g\circ f)(2)=(2)^4+4(2)^2+2=34$
