Question

Determine if f(x) and g(x) are inverses of each other. To determine this, find f(g(x)) and g(f(x))Let f(x) = + 9 and g(x) = 2. - 18.Of(x) and g(x) are inverses.Of(x) and g(x) are NOT inverses.

Answer 1

To determine f(g(x));

$\begin{gathered} f(g(x))=2(\frac{x}{2}+9)-18 \\ f(g(x))=2(\frac{x+18}{2})-18 \\ f(g(x))=x+18-18 \\ f(g(x))=x \end{gathered}$

To determine g(f(x));

$\begin{gathered} g(f(x))=\frac{(2x-18)}{2}+9 \\ g(fx))=(\frac{2x}{2}-\frac{18}{2})+9 \\ g(f(x))=\frac{2x}{2}-9+9 \\ g(f(x))=\frac{2x}{2} \\ g(f(x))=x \end{gathered}$

They are NOT inverses, as shown from the results.