Answer
a. $x^4-6x^2+10$
b. $x^4+2x^2-2$
c. $2$
d. $22$
Work Step by Step
Given $f(x)=x^2+1$ and $g(x)=x^2-3$, we have:
a. $(f\circ g)(x)=(x^2-3)^2+1=x^4-6x^2+10$
b. $(g\circ f)(x)=(x^2+1)^2-3=x^4+2x^2-2$
c. $(f\circ g)(2)=(2)^4-6(2)^2+10=2$
d. $(g\circ f)(2)=(2)^4+2(2)^2-2=22$
