Question

If f(x) = *-3, 6(x)= x+3, and h(x) = 2x+1, what is (gonof)(x)?o (gonof)(x) = 3x-3X-6o (g• hof)(x) – Bx-6o (go hof)(x) = 2x+48x+1o (g họf)(x) = 2x + 1

Answer 1

The given functions are

f(x) = (x - 3)/x

g(x) = x + 3

h(x) = 2x + 1

The first step is to simplify (h.f)(x). This means that we would substitute x = (x - 3)/x into h(x) = 2x + 1. It becomes

2(x - 3)/x + 1

= (2x - 6)/x + 1

= (2x - 6 + x)/x

= (3x - 6)/x

The next step is to find (g.h.f)(x) by substituting x = (3x - 6)/x into g(x) = x + 3. It becomes

(3x - 6)/x + 3

= (3x - 6 + 3x)/x

= (6x - 6)/x

Thus,

(g.h.f)(x) = (6x - 6)/x

The second option is correct