Problem

n.)
ali $x$ in the domain of the composition.
(b)
\[
\begin{array}{l}
f(x)=-\frac{2}{x}, x \neq 0 \\
g(x)=\frac{2}{x}, x \neq 0 \\
f(x(6))=\square \\
g(x(6))=\square
\end{array}
\]

Answer

Expert–verified
Hide Steps
Answer

\(\boxed{f(6) = -\frac{1}{3}, g(6) = \frac{1}{3}}\)

Steps

Step 1 :The problem is asking for the values of the functions \(f(x)\) and \(g(x)\) when \(x\) equals 6. Since the functions are defined for all \(x\) not equal to 0, we can directly substitute \(x = 6\) into the functions to find the values.

Step 2 :Substitute \(x = 6\) into the function \(f(x) = -\frac{2}{x}\), we get \(f(6) = -\frac{2}{6} = -\frac{1}{3}\).

Step 3 :Substitute \(x = 6\) into the function \(g(x) = \frac{2}{x}\), we get \(g(6) = \frac{2}{6} = \frac{1}{3}\).

Step 4 :\(\boxed{f(6) = -\frac{1}{3}, g(6) = \frac{1}{3}}\)

link_gpt