For the function $f\left(x\right)=\frac{1}{x-2}$, determine each of the following values.

1. What is $f(4)$? (This means calculate the output of the function when $x = 4$.)

   Step 1 (a):

   Substitute $4$ for each $x$.

   $f(4)=\frac{1}{4-2}$

   Step 2 (a):

   Simplify. $x − 2$

   Answer (a):

   $f(4)=\frac{1}{2}$

2. What is $x$ when $f(x) = 1$? (This means determine the input that gives an output of $1$.)

   Step 1 (b):

   Substitute $1$ for $f(x)$.

   $1=\frac{1}{x-2}$

   Step 2 (b):

   Solve for $x$ (multiply both sides by $x − 2$).

   Answer (b):

   $x = 3$