Function Notation
Function Operations
Functions operations can be evaluated with either values of the domain or expressions.
Example 1 Given that f(x) = 3x + 2, find f(x + h) - f(h).
Step 1 . Evaluate f(x + h).
f () = 3( ) + 2
f (x + h) = 3(x + h) + 2
f(x + h)=3x+3h+ 2
Step 2. Evaluate f(h)
f () = 3( ) + 2
f (h) = 3h + 2
Step 3 . Subtract and simplify. Substitute the above expressions using the subtraction rule and combine like terms.
f (x + h) - f(h)
[3x + 3h+ 2] - [3h + 2]
3x+ 3h+ 2- 3h - 2
3x + 6h
f(x + h) - f(h) = 3x + 6h