## College Algebra 7th Edition

$1+\sqrt{x}$
We are given: $f(x)=\sqrt{1-x}$, $g(x)=1-x^{2}$ and $h(x)=1+\sqrt{x}$ We evaluate: $(f\circ g\circ h)(x)=f(g(h(x)))=f(g(1+\sqrt{x}))=f(1-(1+\sqrt{x})^{2})=f(1-(1+2\sqrt{x}+x))=f(1-1-2\sqrt{x}-x)=f(-2\sqrt{x}-x)=\sqrt{1-(-2\sqrt{x}-x)}=\sqrt{1+2\sqrt{x}+x}=\sqrt{(1+\sqrt{x})^{2}}=1+\sqrt{x}$