Find the functions of fog, gof, fof, and fog and their domains.

Question

f(x)= square root of x, g(x)=2/x-4

Answer 1

Hi Ruby,

fog(x) = f[g(x)] = f[2/(x-4)] = sqrt(2/(x-4)), domain is any non negative x value greater than 4.

gof(x) = g[f(x)] = g[sqrt(x)] = 2 / (sqrt(x) - 4), domain is any non negative x value excluding 16.

fof(x) = f[f(x)] = f[sqrt(x)] = x^(1/4), domain is any non-negative x value.

gog(x) = g[g(x)] = g[2/(x-4)] = 2 / (sqrt(x) - 4) = (2x - 8) / (18 - 4x), domain is any x value excluding 4.5.

Let me know if you have any questions.

Anouk