asnwer is (g o h o f)(x) = 2x - 6/x + 7
step-by-step explanation:
given,
f(x) = x - 3/x
g(x) = x + 3
h(x) = 2x + 1
we need to find : (g o h o f)(x)
we can write (g o h o f)(x) = g[ h{ f(x) } ]
so first we find h{f(x)}
h{f(x)} = f(x) + 3 = (x - 3/x) + 3
h{f(x)} = x - 3/x + 3
now we find g[ h{ f(x) } ].
g[ h{ f(x) } ] = g(x - 3/x + 3) {plug h{f(x)} = x - 3/x + 3 in g[h{f(x)}] }
g(x - 3/x + 3) = 2 (x - 3/x + 3) + 1
= 2x - 6/x + 6 + 1
= 2x - 6/x + 7
hence we get (g o h o f)(x) = 2x - 6/x + 7