Question

For each pair of functions f and g below, find f(g(x)) and g(f(x)).

Answer 1

Answer:

a)  f(g(x)) = $\frac{1}{2(\frac{1}{2x} )}$ = $\frac{1}{\frac{1}{x} } }$ = x

    g(f(x)) = $\frac{1}{2(\frac{1}{2x} )}$ = $\frac{1}{\frac{1}{x} } }$ = x

    f and g are inverses

b)   f(g(x)) = x + 3 + 3 = x + 6

     g(f(x)) = x + 3 + 3 = x + 6

     f and g are not inverses

Step-by-step explanation:

a)

f(g(x)) = $\frac{1}{2(\frac{1}{2x} )}$ = $\frac{1}{\frac{1}{x} } }$ = x

g(f(x)) = $\frac{1}{2(\frac{1}{2x} )}$ = $\frac{1}{\frac{1}{x} } }$ = x

Since f(g(x)) = g(f(x)) = x, then f and g are inverses

b)

f(g(x)) = x + 3 + 3 = x + 6

g(f(x)) = x + 3 + 3 = x + 6

Since f(g(x)) = g(f(x)) ≠ x, then f and g are not inverses