Answer
a. $f \circ g=x$,
b. $g \circ f=|x|$,
c. $(f \circ g)(2)=2$
d. $(f \circ f)(2)=26$
e. $f \circ g \circ f=1+x^2$
f. $g \circ f \circ g=\sqrt {x-1}$
Work Step by Step
$f(x)=1+x^2$,
$g(x)=\sqrt {x-1}$,
a.
$f \circ g=1+(\sqrt {x-1})^2=1+x-1=x$,
b.
$g \circ f=\sqrt {x^2}=|x|$
c.
$(f \circ g)(2)=2$
d.
$f \circ f=1+(1+x^2)^2=x^4+2x^2+2$
$(f \circ f)(2)=2^4+2(2)^2+2=26$
e.
$(f \circ g \circ f)(x)=f(g(f(x))=f(|x|)=1+x^2$
f.
$(g \circ f \circ g)(x)=g(f(g(x))=g(x)=\sqrt {x-1}$
