Answer
$a. g(5s+2)=\sqrt {(5s+2)}$
$b. g(\sqrt x+2)=\sqrt {(\sqrt x+2)}$
$c.3g(5x)=3\times\sqrt {(5x)}$
$d. 1/g(x)=1/(\sqrt x)=\sqrt x/x$
$e.g(g(x))=g(\sqrt x)=\sqrt {(\sqrt x)}$
$f. (g(x))^2-g(x^2)=(\sqrt x)^2-\sqrt x^2$
$g. g(1/\sqrt x)=1/\sqrt {(\sqrt x)}$
$h. g((x-1)^2)=\sqrt {(x-1)}^2=x-1$
$i. g(x+h)=\sqrt {(x+h)}$
Work Step by Step
$a. g(5s+2)=\sqrt {(5s+2)}$
$b. g(\sqrt x+2)=\sqrt {(\sqrt x+2)}$
$c.3g(5x)=3\times\sqrt {(5x)}$
$d. 1/g(x)=1/(\sqrt x)=\sqrt x/x$
$e.g(g(x))=g(\sqrt x)=\sqrt {(\sqrt x)}$
$f. (g(x))^2-g(x^2)=(\sqrt x)^2-\sqrt x^2$
$g. g(1/\sqrt x)=1/\sqrt {(\sqrt x)}$
$h. g((x-1)^2)=\sqrt {(x-1)}^2=x-1$
$i. g(x+h)=\sqrt {(x+h)}$
$$\boxed{\text{Please see additional work shown in attached image.}}$$
