Question

6) For each pair of functions, find

f gx, gf x, f f xand ggx

a)
f x x g x x      ; 4 2  

b)
  ;   1

Answer 1

a)

f[g(x)] = f[g(x)] = f[-4] = -(4) = -4

g[f(x)] = g[f(x)] = g[-2] = -2

f[f(x)] = f[f(x)] = f[-2] = -2

g[g(x)] = g[g(x)] = g[-4] = -4

b)

f[g(x)] = f[g(x)] = f[1] = -1

g[f(x)] = g[f(x)] = g[-1] = 1

f[f(x)] = f[f(x)] = f[-1] = -1

g[g(x)] = g[g(x)] = g[1] = 1