Question

The function of f and g are defined as

f(x) = 1/x - 1
g(x) = x^3

a. Find the composite function f[g(x)]
b. The value of f[g(2)]

Answer 1

f(g(x))- 1/x^3-1

1/7

Explanation:

Given the functions defines by;

f(x) = 1/x - 1

g(x) = x^3

a) Find f(g(x))

f(g(x)) = f(x^3)

Replace x with x^3 in f(x) as shown;

f(x^3) = 1/x^3 - 1

f(g(x))- 1/x^3-1

b) Substitute x = 2 into the result;

f(g(2)) = 1/2^3 - 1

f(g(2)) = 1/8-1

f(g(2)) = 1/7

Hence f(g(2)) = 1/7