a)The functions f and g are defined by f(x) = root x for x > 0; g(x) = x - 1 for all values of x.
i.)Write down expressions for fg(x) and gf(x).
> fg(x) = root x - 1
> gf(x) = root x - 1
ii.) Verify that x = 1 => fg(x) = gf(x)
>??????
a)The functions f and g are defined by f(x) = root x for x > 0; g(x) = x - 1 for all values of x.
i.)Write down expressions for fg(x) and gf(x).
> fg(x) = root x - 1
> gf(x) = root x - 1
ii.) Verify that x = 1 => fg(x) = gf(x)
>??????
$\displaystyle f(x) = \sqrt{x}$ , $\displaystyle x > 0$
$\displaystyle g(x) = x - 1$
I assume you mean function composition by the notation "fg(x) and gf(x)"
$\displaystyle f[g(x)] = f(x-1) = \sqrt{x-1}$
$\displaystyle g[f(x)] = g(\sqrt{x}) = \sqrt{x} - 1$
you should be able to see that $\displaystyle f[g(1)] = g[f(1)] = 0$