I have a test in my pre-calculus class soon and i was wondering if anyone could help with a couple problems?

Question

1. Let f(x)=square root of x-2 g(x)= 1/x

a. (g(f(x))

b. (f(g(x))

2. h=cube root of (x cubed-1)+1

a. (h(k(x))

b. (k(h(x))

Answer 1

1.

y = f(x) = sqrt(x - 2)

z = g(y) = 1/y

g(f(x)) = 1/f(x) = 1/ sqrt(x - 2)

f(g(x)) = sqrt ( g(x) - 2) = sqrt( 1/x - 2)

2.

h = (x^3 - 1)^(1/3) + 1

k(x) = undefined

h(k(x)) = (k(x)^3 - 1)^(1/3) + 1

k(h(x)) = k( (x^3 - 1)^(1/3) + 1)